3.2 Warmup

1. Determine the measurement of the indicated side. Express your answer to the nearest

tenth of a centimetre.

a) b)

2. Determine the value of each indicated angle, to the nearest degree.

a) b)

3. Mary wishes to determine the height of the tree in her yard. She measures the angle of

elevation to the top of the tree to be 25° at a point 20 m from the base of the tree.

How tall is the tree, to the nearest tenth of a metre?

4. Matt is 1.65 m tall and his shadow is 1.43 m long. Determine the angle of elevation of the

sun, to the nearest degree.

FCP 10 Date:________________

3.1 The Sine and Cosine Ratios

To use the tangent ratio to find AB, we would have

to:

Instead of using the tangent ratio to find the missing side, there are other

trigonometric ratios that make use of the hypotenuse:

It is still important to remember which is the angle of interest!

Sine Ratio

- abbreviated as :

sin A =

sin B =

Cosine Ratio

- abbreviated as :

cos A =

cos B =

Tangent Ratio

- abbreviated as :

tan A =

tan B =

Remember:

12m

A

B 33

o

C

A

B C

A

B C

A

B C

This is

SOH CAH TOA!!

D. Find the sine and cosine of A for the following right triangles:

E. Evaluate each to 4 decimal places using your calculator

sin 32o

sin 30o cos 72o cos 60o sin 80o

F. Find each missing angle. Write the inverse step

tan A = 1.287

cos A = .251 sin A = .493 tan A = 0.34

sin A = 13

cos A = 32

tan A = 125

cos A = 43

Note: only tangent can have an absolute value greater than

_____________________

Sine and cosine must be between _________ and __________.

A

10

6

8 A

5

3

4

Solve for each missing variable: 6.4sin 41x

3cos 45x

Joe is flying a kite on the end of a 52m long string. The string makes a 68o angle

with the ground. How high is the kite?

14

8

ɵ

14 9 x

40o

a 10

32o

h

3.3 Warm Up 1. Write each ratio in lowest terms.

a) sin A

b) cos A

c) sin B

d) cos B

2. Evaluate each trigonometric ratio, to four decimal places.

a) sin 35° b) cos 12° c) sin 78° d) cos 85°

3. Determine the measure of each angle, to the nearest degree.

a) 4

5sin A b) cosB 0.1564 c) sinC 0.4540 d) cos 0.6820

4. Determine each length of x. Express your answer to one decimal place.

a)

b)

c)

d)

5. Determine the measure of each indicated angle. Express your answer to the nearest degree.

a) b)

c)

d)

6. If the kite string in the figure is 120 m long, calculate the height of the kite. Express your answer to the

nearest tenth of a metre.

7. Bill is renovating his house. He braces a wall with an 8-ft wall brace, as shown. The distance from the

wall to the lower end of the brace (on the floor) is 2.4 ft. Calculate the angle at which the brace meets

the wall. Express your answer to the nearest degree.