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17-1 The Trigonometric Ratios

Purpose Learn 3 trig ratios (Sin, Cos, or Tan)

for right triangles, so that later on you can

find the missing side, or angle of a right

triangle.

Trigonometry The study of the measurement of

triangles

B

c

a

A

C

b

Sin ltA

Opposite Leg

Hypotenuse

B

c

a

A

C

b

Cos ltA

Adjacent Leg

Hypotenuse

B

c

a

A

C

b

Tan ltA

Opposite Leg

Adjacent Leg

Tan your legs, opp on top

B

c

a

A

C

b

SOHCAHTOA

B

Opposite Leg

Hypotenuse

c

a

A

C

Adjacent Leg

b

Find the sin, cos,and tan of angle A

B

13

5

A

C

12

Fill in the missing lengths for the special right

triangle, and then find the sin, cos, and tan of

a 30º,60º, 45º

30

45

1

45

60

1

- Pg. 559
- (2acefj,3bdfk,
- 5-8,10,12,18,19)

- Surveying the Uses of Trigonometry
- Some people just do not know how to have fun.

They think everything has to be useful. Luckily,

the sine, cosine, and tangent functions do have a

lot of real-world uses. - Surveyors use the tangent function a lot. For

example, they can use trigonometry to figure out

the distance across rivers. - We first set up a survey post directly across the

river from some landmark (like a tree). Then we

head downstream a distance that we can measure

in this case, 400 meters. Thats the red

horizontal line in the drawing. - Now we take a sighting on the tree from

downstream. Thats the black line in the drawing.

The surveying instruments will tell us what our

sighting angle is. In this case, its 31 degrees.

- We know from the previous page that the tangent

of 31 degrees is equal to the length of the blue

line divided by the length of the red line (400

meters). So, if we multiply the tangent of 31

degrees by 400 meters, well get the distance

across the river. - The tangent of 31 degrees is about 0.60. That

means that the distance across the river is 0.6

times 400 meters, or 240 meters. - Real world alert! Wouldnt it have been simpler

to just tie a rope to the tree, climb into a

boat, go across the river, and measure how much

rope you trailed out? In this case, it actually

might be a good idea to physically cross the

river to check the answer from our math. This

gives us confidence that trigonometry really

works. - After all, sometimes the real world gives us a

river that is too difficult to cross or a cliff

too dangerous to climb. In these cases the

physical approach isnt possible. We need

trigonometry--a mathematical technique we can

trust for the answers we need.

(No Transcript)

6v3

- Sin ltL ____
- 12
- 2.( )ltC 6
- 6v3
- 3. What are the measures of ltC and ltL
- 4. Find the cosltA
- 5. Find the sin ltK
- 6. Simplify this expression by evaluating it
- tan 45º
- Cos 60

T

C

6

12

L

13

13

A

K

10

17.2 Numerical Trigonometry

- Purpose
- Use Sin, Cos, or tan to find measurements of a

missing side of a right triangle, or an acute

angle of a right triangle given two of the sides

Trig table on page 567

- Use your table and your calculator to find these

values - 1. sin 35º
- 2. cos 57º
- 3. tan 25º
- Find ltA for each
- 4. sinltA .45
- 5. cos ltA .26
- 6. Tan ltA 5

Find X

15

x

22º

Find X

20

32º

x

Find X

13

17º

x

H

65º

100 ft

Find X

13

17º

x

- Pg. 564
- (1a-e,2acegi,
- 3-6,8,11,15-17,19)