Date

: 2/7

Aim

: To use trigonometric ratios for indirect measurements of right triangles.

Trigonometry

• Derived from Greek words,

“trigonon"

triangle, and

"metria”

which means which means measure.

•

Trigonon metria

= “triangle measurement” • fold.

Sine

comes from the Latin word

sinus

meaning a curve or •

Cosine -

was originally written "

co.sine,"

short for

COMPLEMENTI SINUS

: the sine of the complementary angle.

•

Tangent -

comes from the Latin word

tangens

straight line which touches a circle at one point. which is a

Triangle Ratios Sine of

 

length of leg Opposite



length of Hypotenuse Cosine of

 

length of leg Adjacent



length of Hypotenuse Tangent of

 

length length of leg Opposite



of Adjacent



• SOH • CAH • TOA

SOH CAH TOA is mnemonic for:

Sin  Opposite Hypotenuse Cos  Adjacent Hypotenuse Tan  Opposite Adjacent

Sin

A



a c

Cos

A



b c

Tan

A



a b

Trigonometry

B C

a b c

A

Using Trigonometry

• Find the lengths of

a

and

c

.

A

Sin 7 3   29

c c

 29 Sin 73 

c

 30 .

3 Tan 7 3   29

a a

 29 Tan 73 

a

 8 .

9 29

c

C

73 

a

B

Try on your own:

y

x

tan 32 o tan 32 tan 32 o o

x

= opp. adj.

= 11

x

= 11 = 11 tan 32 o

x

11 0.6249

x

17.6

Sin 32   11

y y

 11 Sin 3 2 

y

 20 .

8

Using Trigonometry

• A 20-ft wire supporting a flagpole forms a 35 o angle with the flagpole. To the nearest foot, how high is the flagpole?

Cosine Ratio Cos 35  

x

20

x

 20 ( Cos  35  )

x

 16 ft 20 35 

x

You want to build a skateboard ramp with a length of

14

feet and an angle of elevation of

26°

. You need to find the height and length of the base of the ramp

.

sin 26 sin 26 o o 6.1 ft.

= = 14 sin 26 o

x x

=

x

cos 26 o = adj. hyp.

cos 26 o =

y

14 14 cos 26 o =

y

12.6 ft.

y

Date

: 2/8

Aim

: To use these ratios for indirect measurements of right triangles.

Do Now:

Find

h

.

Find the height

h

of the lamppost to the nearest inch.

tan 70 o = opp. adj.

tan 70 o =

h

40 40 tan 70 o =

h

109.9

h

ANSWER The lamppost is about

110

inches tall.

• Mount Everest – 29, 029 feet

• The Burj Khalifa, Dubai – 2717 feet

• Angel, Salto – Venezuela - 3,212 feet

Clinometer

Angle of Elevation 42 ° 42 ° Angle of Depression

•

The angle of elevation

of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).

• If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the

angle of depression

.

θ – angle of interest Which angle is the angle of elevation? Which angle is the angle of depression ?

A - angle of elevation B – angle of depression B θ A

How tall is the Empire State Building?

Exact Answer: 1,250 feet tall 76.5

° 300 ft

Since Mount Everest is 29, 029 feet tall, how far was Ms. Psillos from the mountain, if her angle of elevation was 55 °?

20,326.3 feet

Ms. Psillos is looking up at the waterfall in Angel, Salto – Venezuela, which is 3,212 feet tall, and has an angle of elevation of 82 °. She wants to know the distance that her line of sight makes to the top of the waterfall?

3,243.6 feet

Using Trigonometry

• Find

m



R

to the nearest degree.

Tangent Ratio

R

Tan 

R

 47 41 Tan 

R

 1 .

146 41

S

Tan  1 1 .

146 

m



R R

 49  47

T