Transcript Warm=up 1. Given an adjacent side and the hypotenuse, which trig function do you use? cos 2.

Warm=up
1. Given an adjacent side and the hypotenuse, which trig function do
you use?
cos
2. Given an opposite side and the hypotenuse, which trig function do
you use?
sin
3. Given both the opposite side and the adjacent, which trig function
do you use?
tan
4.
Standardized Test Practice:
In the right triangle which
trig function would you use to find CD with C?
C
D
37°
5
A
cos
B
sin
C
tan
Click the mouse button or press the
Space Bar to display the answers.
D
sec
E
Warm=up
Find x.
x ≈ 53.14°
5.
10
x°
6
32
6.
33°
Click the mouse button or press the
Space Bar to display the answers.
x ≈ 17.43
x
Right Triangle Trigonometry
Trig Definitions
• Sin (angle) =
Opposite
---------------Hypotenuse
S-O-H
• Cos (angle) =
Adjacent
---------------Hypotenuse
C-A-H
• Tan (angle) =
Opposite
---------------Adjacent
T-O-A
Ways to Remember
SOHCAHTOA
• S-O-H
Some Old Hillbilly
Caught Another Hillbilly
Throwing Old Apples
• C-A-H
• T-O-A
Some Old Hippie
Came A Hoppin’
Through Our Apartment
Extra-credit:
Your saying
Steps to Solve Trig Problems
• Step 1: Draw a triangle to fit problem
• Step 2: Label sides from angle’s view
– H: hypotenuse
– O: opposite
– A: adjacent
• Step 3: Identify trig function to use
– Circle what values you have or are looking for
– SOH
CAH
TOA
• Step 4: Set up equation
• Step 5: Solve for variable
Example 1
SOH-CAH-TOA (Sin θ = O/H, Cos θ = A/H, Tan θ = O/A)
θ is a symbol for an angle
Remember:
Sin 90° is 1
Cos 90° is 0
Tan 90° is undefined
Example 1:
When looking for an angle use the
inverse of the appropriate trig function
(2nd key then trig function on your
calculator)
12
x°
8
tan x° = 12/8
x = tan-1 (12/8)
x = 56.31°
12 is opposite the angle x; and 8 is
adjacent to it:
opp, adj  use tangent
Example 2
SOH-CAH-TOA (Sin θ = O/H, Cos θ = A/H, Tan θ = O/A)
θ is a symbol for an angle
Remember:
Sin 90° is 1
Cos 90° is 0
Tan 90° is undefined
Example 2:
17
52°
When looking for a side use the appropriate trig
function (based on your angle and its
relationship to x, and your given side).
17 is opposite of the angle and x is adjacent to it:
opp, adj  use tangent
x
tan 52° = 17/x
x tan 52° = 17
x = 17/tan 52°
x = 13.28
Example 3
SOH-CAH-TOA (Sin θ = O/H, Cos θ = A/H, Tan θ = O/A)
θ is a symbol for an angle
Remember:
Sin 90° is 1
Cos 90° is 0
Tan 90° is undefined
Example 3:
13
x
13 is the hypotenuse (opposite from the 90
degree angle) and x is opposite from given
angle:
opp, hyp  use sin
47°
sin 47° = x/13
13 sin 47° = x
9.51 = x
Check Yourself
• You have a hypotenuse and an adjacent side
14.34
Cos
Use: _______
Solve:
x
=
___
25
x
55°
• You have an opposite and adjacent side
21.42
Tan
Use: _______
Solve: y = ___
15
35°
y
• You have an opposite side and a hypotenuse
26.15
Sin
Use: _______
Solve:
z
=
___
z
15
35°
Example 4
EXERCISING A fitness trainer sets the incline on a
treadmill to 7°. The walking surface is 5 feet long.
Approximately how many inches did the trainer raise the
end of the treadmill from the floor?
Step 1:
Step 2:
Step 3:
Step 4:
Draw a triangle to fit problem
Label sides from angle’s view
Identify trig function to use
Set up equation
Step 5: Solve for variable
Opp
SO/H
CA/H
TO/A
Opp
y
sin 7° = -------- = ----Hyp
60
Let y be the height of the treadmill from the floor in inches.
The length of the treadmill is 5 feet, or 60 inches.
Example 4 cont
Multiply each side by 60.
Use a calculator to find y.
KEYSTROKES: 60
SIN
7
ENTER
7.312160604
Answer: The treadmill is about 7.3 inches high.
Example 5
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
the ramp is about 4.8°, how high does the ramp rise
off the ground to the nearest inch?
Answer: about 15 in.
Trig Practice
1) Identify what you are trying to find (variable) – Side or Angle
2) Relate given (opp, adj, hyp, angle) to the variable
3) Solve for variable
1.
Side, x opposite 30° and 24 is the hyp
 sin 30 = x/24
24
x
x = 24 sin 30 = 12
30°
2.
20
15
Angle, x opposite 20 leg and 15 is adj leg
 tan x = 20/15 x = tan-1 (20/15) = 53.1
x°
3.
x
60°
30
Side, x adjacent 60 and 30 is the hyp
 cos 60 = x/30 x = 30 cos 60 = 15
Trig Practice cont
1) Identify what you are trying to find (variable) – Side or Angle
2) Relate given (opp, adj, hyp, angle) to the variable
3) Solve for variable
4.
13
x
Side, x opposite 49 and 13 is the hyp 
sin 49 = x/13 x = 13 sin 49 = 9.81
49°
12
5.
45°
x
6.
x°
12
18
Side, x is hypotenuse and 12 is adj leg 
cos 45 = 12/x x = 12/(cos 45) = 12√2
Angle, x is opposite 12 and 18 is hyp  sin
x = 12/18 x = cos -1 (12/18) = 48.2
Trig Practice cont
1) Identify what you are trying to find (variable) – Side or Angle
2) Relate given (opp, adj, hyp, angle) to the variable
3) Solve for variable
7.
16
Side, x is adjacent 54 and 16 is opp
 tan 54 = 16/x x = 16/(tan 54) = 11.62
54°
x
8.
Angle, x is opposite 12 and adj to 10
 tan x = 12/10 x = tan-1 (12/10) = 50.2
12
x°
10
Summary
• Summary:
– Trigonometric ratios can be used to find
measures in right triangles
– Identify what you are trying to find (variable)
– Side or Angle
– Relate given (opp, adj, hyp, angle) to the
variable
– Solve for variable