Transcript Using the hp33s - lsaw

Using the hp33s
For Land Surveying
Computations
by Jon B. Purnell, PLS
©2010 Alidade Consulting
Synopsis
• Strategies
• Capabilities and
Limitations
• Operating Essentials
• Statistics Functions
• Traverse and Inverse
• Memory and Variables
• Equation Solver
Capabilities
and Limitations
• User programmable
– 31K of memory for
programs, variables and
user equations
• 27 storage registers
– For variables/data
• Integrated equation
Solver utility
• RPN or Algebraic entry
modes
Capabilities
and Limitations
• 3rd Party surveying
applications are
available
– http://www.softwareby
dzign.com/
• Legal for LSIT exam
– http://www.ncees.org/
exams/calculators/
0.00000000
0.00000000
The Keyboard
Press [TEAL] +
[key] to access Teal
functions
Press [key] alone to
access“unshifted”
functions
Press [PURPLE] +
[key] to access Purple
functions
Press key when
prompted for “Alpha”
input
Press to power [ON] or to clear an entry
Press [PURPLE] [ON] to turn unit OFF
0.00000000
0.00000000
The Keyboard
Press to select operating modes: DEGrees,
GRADs, RADians, and separators
Press to select DISPLAY formats: FIXed,
ENGineering notation, SCIentific notation,
or ALL (automatic formatting)
Cursor pad—click up, down, left or right to
choose menu options, or scroll
10.00000000
FIX 2SCI
0.0000
3FIX
0.00000000
E N4 G 4 A L L
0.0000
Setting and Changing
Display Formats
Press to open DISPLAY menu
Options appear on menu. Underlined option
= current selection
Use Cursor Pad to select display mode, or
press [1] for FIXed, [2] for SCIentific, [3]
for ENGineering, or [4] for ALL
EXAMPLE: to set display to show 4 FIXed
decimal places:
1. Press [DISPLAY], then [1], then [4]
10.0000
D E G 2 RAD
0.0000
30.0000
GRAD 4 . 5,
0.0000
Setting and Changing
Angular Mode Format
Press to open MODES menu
Options appear on menu. Underlined option
= current selection
Use Cursor Pad to select mode, or press [1]
for DEGrees, [2] for RADians, [3] for
GRADS, or choose [4] to use dot& comma as
decimal point and 1000’s seperator
EXAMPLE: to set unit to work in DEGrees:
1. Press [MODES], then [1]
Mode icons:
ALGebraic, RPN and EQuatioN entry modes,
GRADs and RADians angular modes
Program “Flag”
indicators
Icons: [Teal]
and [Purple]
keys
System Busy
The
Display
“Alpha” keys
Programming
active
mode active
ERROR!
Current numeric system: HEXidecimal,
OCTal or BINary. Blank = Decimal
Two lines of data
HYPerbolic mode is active
Low
battery
Scrolling mode
is active
RPN: Reverse Polish Notation =
Math without Parentheses
• Evaluate 20 / 2+3
• RPN:
– 20 [ENTER] 2 [ENTER] 3 [+] [/]
(Result is 4)
• Algebraic:
– 20 [/] [(] [2] [+] [3] [)] [=]
(Result is 4)
Order of operations and your
calculator
=13
20  2  3
20  (2  3)
=4
=4
20
23
20
(2  3)
20
3
2
=4
Not all of these expressions yield
the same answer!
Be careful how you write and enter
the expression!
=13
“ALG” should appear
here
Algebraic Mode
• Set up your calculator to operate in
the ALG (Algebraic) mode
2. Press [x√y]
1. Press the [Purple] key
20  2 + 3 =
20
20.0000
10.0000
13.0000
Back
to our problem…
• Evaluate the expression
20 / 2+3
1. Key in “20”
2. Press the [division]
key
3. Key in “2” and press
the [addition] key…
…what happens?
4. Key in “3” and press
[ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
20  ( 2 + 3 ) =
20
5320.0000
4.0000
Let’s try it again…
• Evaluate the expression
20 / (2+3)
1. Key in “20”
2. Press the [division]
key
3. Press the [Purple]
key and then press
the [+/-] key
4. Key in “2+3”
5. Press the [Purple]
key and then press
the [E] key, and
press [ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
Are the results the
same as before?
What’s different?
11 keystrokes!
“RPN” should appear
here
RPN: Math without
parentheses
• Set up your calculator to operate in
the RPN (Reverse Polish Notation)
mode
2. Press [x√y]
1. Press the [Teal] key
Using RPN
0.0000
20.0000
2.0000
20
4.0000
52.0000
20.0000
3
• Evaluate the expression
20 / (2+3) using RPN
1. Key in “20”
2. Press the [ENTER]
key
3. Key in “2” and press
[ENTER]
Did the calculator
evaluate the
expression using
the rules of the
order of
operations?
4. Key in “3” and press
the [addition] key
5. Press the [division]
key
8 keystrokes!
The Stack
0.0000
0.0000
0.0000
0.0000
T register
Z register
Y register
X register
• Four “registers” (X,Y,Z
and T) for temporary
storage of values and
intermediate results
• X and Y registers
visible on the display
• Z and T registers, not
visible
• Operations performed
on values in X and Y
registers
20 / (3+2) on the Stack
0.0000
20.0000
0.0000
3.0000
20.0000
0.0000
0.0000
20
20.0000
23.0000
5.0000
4.0000
T register
Z register
Y register
X register
• Key in “20”
• Press [ENTER]
• Key in “3”, Press
[ENTER]
• Key in “2”
• Press [+]
• Press []
Stack Functions
“Roll Down” (values in stack drop down 1
register, value in X register goes to top
(T register)
“X-Y Exchange” (values in X and Y registers
trade places)
“Last X” (recalls last value stored in X register)
Press [Teal] [ENTER] to execute
Some Functions that
Operate on Values
in the X Register
• Key in a number, execute
the function
“1 over X” [1/X]
“Square root of X” [√X]
“X Squared” [X2]
“Trig Functions” [SIN]
[COS] [TAN]
[ASIN] [ACOS]
[ATAN]
Unit Conversions
• The hp33s ships with several built in
unit conversions
– Sexagesimal Units (Decimal Degrees and
Degrees Minutes and Seconds)
– Centigrade and Farenheit
– Inches and Centimeters
Sexagesimal Units
• When finding the Sine, Cosine or
Tangent of an angle, you must:
– Enter the value in degrees, minutes and
seconds…
– …then, convert the value to decimal
degrees…
– …then get the Sine, Cosine or Tangent
0.0000
20.0910
20.1528
0.9388
Finding a Sine,
Cosine or Tangent
Find the Cosine of 20º09’10”
Key in the value in D.MS format: 20.0910
Convert the D.MS value to Decimal
degrees: Press the [TEAL] key, then
press [HR]
Result is 20.1528°
Press [COS]
Result is 0.9388
(rounded!)
Sexagesimal Math
• When adding, subtracting, multiplying
or dividing, (etc.) an angle, you must:
– Enter the values in degrees, minutes and
seconds…
– …then, convert the values to decimal
degrees…
– …then perform the operation
– …then convert the result to D.MS
format
5.2515
5.2514
0.0000
5.2514
2.5
1.2500
6.5643
6.3351
Problem: Find the angle from a PC to a
POC at
525.14 feet from the
PC
Sexagesimal
Math
(degree of curvature = 2°30’)
Example
1
Solution: Angle = 5.2514 x (2°30’) /2
Key in the value “5.2514”, press [ENTER]
Key in the value “2.30”, press the [TEAL]
key, then press [HR]
Key in the value 2, press the [] key
Press the [x] key. Result is 6.5643°
Convert result to D.MS format:
Press [PURPLE] key, then press [HMS]
Result is 6.3351
which is 6°33’51”
0.0000
0.0000
Sexagesimal Math
Example 2
Problem: Find the Weighted Mean
Azimuth of Line 1 and Line 2
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
Solution =
Weighted _ Azimuth 
 Azm1 Dist 1   Azm2  Dist 2
Dist 1  Dist 2
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
97.0892
0.0000
63776.9027
92.9347
63,776.9027
97.0521
97.0892
656.89
63776.9027
92.9347
2607.0000
242280.8208
306,057.7235
Sexagesimal Math
Solution =
Example

 

Weighted _ Azimuth 
Azm1  Dist 1  Azm2  Dist 2
Dist 1  Dist 2
Key in the value “97.0521”, press the [TEAL]
key, then press [HR], then press [ENTER]
Key in the value “656.89”…then press the [x] key
Key in the value “92.5605”, press the [TEAL]
key, then press [HR], then press [ENTER]
Key in the value “2607.00”…then press the [x] key
….next, press the [+] key
The result, 306,057.7235 is the numerator in the
equation….
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
656.8900
306,057.7235
0.0000
656.8900
2607.00
3263.8900
93.7708
93.4615
Sexagesimal Math
Solution =
Example

 

Weighted _ Azimuth 
Azm1  Dist 1  Azm2  Dist 2
Dist 1  Dist 2
Next, key in the value “656.89”,and press [ENTER]
Key in the value “2607.00”…then press the [+]
key…the result, 3263.8900 is the denominator
in the equation….
Press the [] key…the result 93.7708° is the
weighted mean azimuth of the line in Decimal
Degrees
Convert result to D.MS format:
Press [PURPLE] key, then press [HMS]
The result is 93°46’15”
Statistics functions
•
•
•
•
•
Entering observations
Getting n
Getting the mean of the set
Standard deviation of a population
Standard deviation of a sample
Statistics Functions
Function Description
Keystrokes
S
Enter observations into stats registers
[
S-
Delete observations from stats registers
[TEAL] [
Clear stats registers
[TEAL] [CLEAR] [4]
View SUMMATIONS Menu
[PURPLE] [SUMS]
n
Number of observations in data set
Access via SUMS menu
Sx
Sum of x values
Access via SUMS menu
Sy
Sum of y values
Access via SUMS menu
Sx2
Sum of squared x values
Access via SUMS menu
Sy2
Sum of squared y values
Access via SUMS menu
SCLEAR
SUMS
S]
S-]
Summary Statistics Functions
Function Description
Keystrokes
View MEANS Menu
[PURPLE] [ x y ]
x
Mean of x values
Access via MEANS menu
y
Mean of y values
Access via MEANS menu
xw
Weighted mean of x values
Access via MEANS menu
View Standard Deviation Menu
[PURPLE] [S,s]
Sx
Sample Standard Deviation of x values
Access via SD menu
Sy
Sample Standard Deviation of y values
Access via SD menu
sx
Population Standard Deviation of x values
Access via SD menu
sy
Population Standard Deviation of y values
Access via SD menu
xy
S,s
Problem: Find the Weighted Mean
Azimuth of Line 1 and Line 2
Statistics Example 1
10.0000
656.8900
x2607.0000
X y x2WVARS
30.0000
656.8900
97.0892
1.0000
2607.0000
92.9347
2.0000
93.7708
93.4615
ALL 4 S
Line 1 = 97°05’21” – 656.89 feet
Line 2 = 92°56’05” -2607.00 feet
Clear STATS Registers, press: [TEAL] [CLEAR] [4]
Key in “656.89”, press [ENTER]
Key in “97.0521”, press [TEAL] [HR]
Press [ S]
Key in “2607.00”, press [ENTER]
Key in “92.5605”, press [TEAL][HR]
Press [ S]
Press [PURPLE] [YX], and select 3rd option…result
is weighted mean azimuth in Decimal Degrees
Press [ENTER], press [PURPLE] [HMS]…result is
weighted mean azimuth in Deg.MinSec format
Problem: Find the 95% Standard Deviation
of the following set of 20
observations:
Statistics Example 2
Sx Sy sx sy
0.0000
1.9541
0.0000
20.0000
1.9541
1.96
3.8300
No.
1
2
3
4
5
Value
50
51
52
50
59
No.
6
7
8
9
10
Value
52
52
53
52
52
No.
11
12
13
14
15
Value
51
52
52
55
52
No.
16
17
18
19
20
Value
53
52
51
52
54
Clear STATS Registers, press: [TEAL] [CLEAR] [4]
Key in each value from the table, press
[ S] after each entry
Press [PURPLE], [S,s] to view Sample
Standard Deviation (or Sx) at the
1 Sigma level
Press [ENTER] to copy the result to
the X register.
Key in “1.96” and press [multiply].
Result is Standard Deviation of set
at 95% confidence level
Vectors and vector addition
(Traverse and Inverse)
• You can do these COGO computations
with your hp33s (as is, with no
additional programming)
– Compute latitudes and departures, given
the azimuth and length of a line
– Compute azimuth and distance, given the
coordinates of the end points of a line
– Carry coordinates (traverse)
Traversing with your hp33s
(STATS method)
•
There are a couple of ways to do this…here is one
approach that uses the STATS registers for storing the
current coordinate
1.
2.
3.
4.
5.
6.
7.
8.
9.
Clear the STATS registers
Load starting Northing and Easting into STATS registers
Key in an azimuth in D.MS format
Convert the azimuth to decimal degrees format
Enter a distance
Convert from Polar to Rectangular notation
Exchange contents of X<>Y registers
Add Latitude and Departure to STATS registers
Go to Step 3 and repeat process
Step 7 ensures that the current
Northing will be stored in the
“y” register, and that the
current Easting will be stored in
the “x” register
10.0000
10.6400
15.7514
X
2 VARS
83.8432
0.0000
1000.0000
30.0000
5000
1.0000
10.3824
10.6400
85.31
83.8432
15.7514
ALL 4 
1000
1000.0000
2.0000
Traverse Example
Using STATS registers
Step 1: Clear STATS Registers: press [TEAL]
[CLEAR] [4]
Step 2: Load Start N and E into STATS Registers:
Key in 1000, press [ENTER]. (=Y coordinate = N)
Key in 5000, press [ S]. (=X coordinate = E)
Steps 3-4: Load the Azimuth of the line, 10º38’24”:
Key in 10.3824, press [TEAL] [HR]
Step 5: Load the Distance, 85.31: Key in 85.31
Step 6: Convert from Polar to Rectangular notation:
Press [PURPLE] [Y,X]
Step 7: Exchange contents of x and y registers:
Press [x<>y]
Step 8: Compute and store new coordinate:
Press [ +]
To continue traversing, go to step 3 and repeat.
Traversing with your hp33s
(STATS method)
DISADVANTAGES:
Current coordinate does not appear on “stack”
Must use [SUMS] function to view x (easting) and y
(northing)
Traversing with your hp33s
(Complex Operations Method)
•
Complex Operations can be used to do arithmetic on pairs
of numbers. We’ll use this capability to compute
coordinate pairs (Northings and Eastings)
1.
2.
3.
4.
5.
6.
7.
8.
Load starting Northing and Easting into “y” and “x” registers
Key in an azimuth in D.MS format
Convert the azimuth to decimal degrees format
Enter a distance
Convert from Polar to Rectangular notation
Exchange contents of X<>Y registers
Add Latitude and Departure to “y” and “x” registers using
“complex addition” function
Go to Step 2 and repeat process
Step 6 ensures that the current
Northing will be stored in the “y”
register, and that the current
Easting will be stored in the “x”
register
1083.8432
1000.0000
5000.0000
83.8432
0.0000
10.6400
15.7514
1000.0000
5000
5000.0000
15.7514
5015.7514
0.0000
1000
10.3824
10.6400
85.31
83.8432
Traverse Example
Using Complex math
Step 1: Load Staring N and E into y and x Registers:
Key in 1000, press [ENTER]. (=Y coordinate = N)
Key in 5000, press [ENTER]. (=X coordinate = E)
Steps 2-3: Load the Azimuth of the line, 10º38’24”:
Key in 10.3824, press [TEAL] [HR]
Step 4: Load the Distance, 85.31: Key in 85.31
Step 5: Convert from Polar to Rectangular notation:
Press [PURPLE] [Y,X]
Step 6: Exchange contents of x and y registers:
Press [x<>y]
Step 7: Compute new coordinate:
Press [TEAL] [COMPLEX] [+]
To continue traversing, go to step 3 and repeat.
Traversing with your hp33s
(Complex Operations Method)
ADVANTAGES:
Coordinates appear on the stack. Northing is in the “y”
register, Easting is in the “x” register
DISADVANTAGES:
Coordinates are not stored
No way to “back up” one course
Inversing with your hp33s
(Complex Operations Method)
The Complex Math functions make computing a distance and
direction between two points pretty simple. Here’s how:
1.
2.
3.
4.
5.
6.
Load Northing and Easting of TO point in stack
Load Northing and Easting of FROM point in stack
Use Complex Math to find Latitude and Departure
Exchange contents of X<>Y registers
Convert from Rectangular to Polar notation format
Value in “y” is Θ or direction of line, with respect to north.
If Θ is positive, it = the Azimuth of the line in HR format.
If Θ is negative, add 360° to Θ to get Azimuth of the line in
HR format.
7.
Convert Azimuth of the line to HMS format.
Step 4 ensures that Θ will be
reckoned with respect to North
Inversing Example
Problem: Find azimuth and distance from
Knapp to Sand
390,522.5690
0.0000
392,128.9890
1,606.4200
-10,409.7770
-81.2274
10,532.9978
1,118,227.356_
0.0000
1,107,817.5790
-10,409.7770
1,606.4200
10,532.9978
-81.2274
360
278.7726
278.4621
STATION
NORTHING (Y)
EASTING (X)
"Sand"
392,128.989
1,107,817.579
From "Knapp"
390,522.569
1,118,227.356
To
Steps 1-2: Load Coordinates in stack:
Key in Northing of TO point, press [ENTER]
Key in Easting of TO point, press [ENTER]
Key in Northing of FROM point, press [ENTER]
Key in Easting of FROM point. Stop here!
Step3: Find Latitude and Departure:
Press [TEAL] [CMPLX] [-]
Step 4: Exchange contents of x and y registers:
Press [x<>y]
Step 5: Convert from Rectangular to Polar notation:
Press [TEAL] [Θ,r]
Value in “y” is Θ, or direction of line, with respect to
north, in decimal degrees format
Value in “x” is distance
Memory
• Hp33s has 31K of memory
• You can store
– Numbers
– Equations
– Programs
• 27+ user accessible memory registers
– Registers A though Z, i, (plus STATS registers)
Meters to US Survey Feet:
StoringUSan
1 meter ≈ 3.2808333333
Survey feet
often used number
STO _
You can store this number in a
storage register for later use
Key in value you want to store…
3.28083333333, then press [STO]
Next, choose a register in which to store the
number (select a letter, from A to Z… We
will store this value in register U):
Press [U] to store the value in register U
119,521.1550
0.0000
392,128.9894
337,663.4730
0.0000
119,521.155_
392,128.9894
RCL
337,663.473_
3.2808
1,107,817.5777
_
Using the stored Meters-to-US foot
Math
with
conversion, convert
these
metric
coordinates
to State
Plane values:
Stored
numbers
119,521.155mN, 337,663.473mE
Key in 119521.155
Press [RCL], then [U]
Press [Multiply]
Key in 337663.473
Press [RCL], then [U]
Press [Multiply]
Using Equations
for Problem Solving
• Equations are sets of instructions
that the hp33 can use to perform
computations
• Equations can use values stored in
variables A though Z for their
computations, or they can prompt you
to supply values for the variables
Using Equations
for Problem Solving
• Equations can be used to solve
repetitive problems
• Equations can be used to solve for any
unknown in the equation
• Equations can be stored for future
use, or input on-the fly
• Not all functions are available, see pg.
6-15
Using Equations
for Problem Solving
• ArcLength = 2πR(Δ / 360)
–
–
–
–
Variable assignments:
L = ArcLength
R = Radius
I = Central Angle
• L = 2 x π x R x I/360
0.0000
EQN LIST TOP
0.0000
L=
xLIST
π xx▐
R xx▐I ÷360
L=▐
EQN
L
L=2
▐2x▐
TOP
÷▐
Storing an Equation
Store an equation for solving the
Arc Length of a horizontal curve:
L = 2 x π x R x I/360
Press [Purple] [EQN]
Press [RCL] then [L]
Press [Purple] [=]
Press [2] [multiply]
Press [Purple] [π] [multiply]
Press [RCL] [R] [Multiply]
Press [RCL] [I] [Divide]
Ken in 360, Press [ENTER]
I?
R?
EQN LIST TOP
0.0000
L=
L=
114.59
71.3547
2 x π x R x I ÷360
0.0000
71.2117
142.7075
Use Stored Arc Length equation for
finding the Length of a horizontal
curve with these parameters:
Radius = 114.59 feet
Central angle = 71°21’17”
Using a
Stored Equation
Press [Purple] [EQN]
Scroll up or down if necessary to select
desired equation, and press [ENTER]
At the prompt “R?” key in the curve’s
radius, or 114.59, and press [R/S]
At the prompt, “I?” key in the curve’s central
angle in D.MS format, or 71.2117
Convert the central angle to decimal degrees:
Press [Teal] [HR], then press [R/S]
Result, L is displayed
R=
0.0000
L?
I?
EQN LIST TOP
0.0000
L=
SOLVE
326.30
22.5028
22.8411
818.5072
2 x π_x R x I ÷360
Solving for
an Unknown Variable
Use the Arc Length equation to solve
for curve radius, given:
Arc Length = 326.30
Central angle = 22°50’28”
Press [Purple] [EQN]
Scroll up or down if necessary to select desired
equation (do not press ENTER!)
Press [SOLVE], and then press the key
associated with the variable you need to solve
for, [R] in this case.
At the prompt, “L?” key in the curve arc length,
326.30, then press [R/S]
At the prompt, “I?” key in the curve’s central
angle in D.MS format: 22.5028
Convert the central angle to decimal degrees:
Press [Teal] [HR], then press [R/S]
Selected Equation Mode Operations
Function
Description
Keystrokes
EQN
Enter and leave Equation mode
[Purple] [EQN]
ENTER
Evaluates displayed equation, stores result
in variable on left of equals sign
[ENTER]
RUN/STOP
Prompts for next variable in the equation
[R/S]
CLEAR
Deletes displayed equation from memory
[Teal] [CLEAR]
SOLVE
Solves for a user-specified variable in an
equation
DELETE
Deletes rightmost character in an equation
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100 Foot Arc Definition
Horizontal
Equations
Horizontal Curve
Curve Equations
Name
Equation
Variables
Arc Length
L = 2 x π x R x I ÷ 360
L = Arc Length, R = Raduis,
I = Central Angle in Decimal degrees
SemiTangent
T = R x tan( I ÷ 2 )
T = Semi-tangent, R = Radius
I = Central Angle in Decimal degrees
Long Chord
C = 2 x R x sin( I ÷ 2 )
C = Long Chord, R = Radius
I = Central Angle in Decimal degrees
External
E = ( R ÷ cos(I ÷ 2 )) - R
E = External distance, R = Radius
I = Central Angle in Decimal degrees
Middle
Ordinate
M = R – ( R x cos(I ÷ 2 ))
M = Middle Ordinate, R = Radius
I = Central Angle in Decimal degrees
Degree of
Cruvature
D = 5729.578 ÷ R
D = Degree of Curvature in Decimal
degrees, R = Radius
Test Data
R = 818.51, I = 22°50’28”
L = 326.30, T = 165.35, C = 324.14,
E = 16.53, M = 16.21, D = 7°
Triangles
Name
Equation
Variables
Horizontal
Curve
Equations
Area of Right
triangle
Q=1/2*B*H
Q = Area, B = Base,
H = Height
Area of
Oblique
triangle
Q=.5*A*B*sin(C)
Q = Area, A = Side a, B = side b,
C = Angle C in Decimal degrees
Coslaw
T=acos((B^2+C^2-A^2)
/(2*B*C))
T = Angle A in Decimal degrees, B = side
b, C = side c, A = side a
Hero’s
Formula
Q=SQRT(.5*(A+B+C)*(.5*(A
+B+C)-A)*(.5*(A+B+C)B)*(.5*(A+B+C)-C))
Q = Area, A = side a, B = side b,
C = side c
Pythagorean
Theorem
C = SQRT(A^2+B^2)
Trapezoid
Area
Q=(A+B)*H/2
Q = Area, A = Base 1, B = Base 2, H +
Height
Test Data
Right triangle: a = 60, b = 80,
c = 100, A = 36°52’12”,
B = 53°07’48” C = 90°
Area = 2400
Trapezoid: Base 1 = 100, Base 2 = 80,
Height = 95, Area = 8550
A = side A, B = side B, C = side C
Sliding Area Equation for TI-89 Numeric Solver
11/09/2006 – Jon B. Purnell, PLS
Area of sub-trapezoid to be segregated
from a larger whole – this equation will
compute the height of the height of the
sub-trapezoid given the pre-determined
area of the sub-trapezoid and the height
and two bases of the larger parent
trapezoid.
Enter this in “eqn:” field of TI89 Numeric Solver
Works for all trapezoids. Use to find the distance a parallel line must fall (height of a sub-trapezoid) from
base1 to get a given area, or to find the area of a sub-trapezoid having a given height.
Input Data:
sub-trapezoid area = 3,000,000.00
base1 = 4076.7189
base2 = 1763.1192
ht = 1713.2353
Output: solve for height of sub-trapezoid, h = 857.7407
(NOTE: the computed value “h” is measured from base 1 )
Derived from standard “area-of-a-trapezoid formula”: area = (base1+base2)*height/2 The sliding area
equation substitutes “base1+(base2-base1)/ht*h” for “base 2” in the standard trapezoid area equation (see
standard equation, above).
In a trapezoid, the lengths of the bases are dependent upon their separation (height of the trapezoid) and
upon and the difference in their lengths. It is a linear relationship: (base2-base1)/height describes it; and
it can be thought of as the change in base length per unit of trapezoid height. The relationship can be used
to compute the length of an unknown base of a sub-trapezoid, whose area is given as a fixed value. Then
it is possible to compute the height of a sub-trapezoid whose area has been defined, as in the sample
above.
These kind of problems are often referred to as “sliding side area problems” or “pre-determined area
problems”
• Sample equation
documentation
– Sample problem
– Sketch
– Variable
definitions
– Equation
formated for
input
– Explanation
– Sample data
– Solution
Thanks for your kind attention!
• Contact: Jon B. Purnell, PLS
– [email protected]
– 360-460-8565
• Download this
Presentation at
– www.lsaw-noly.org