7.5 & 7.6– Apply the Sin-Cos-Tan Ratios

Hypotenuse:

Opposite side:

Adjacent side:

Side opposite the reference angle

Side opposite the right angle

Side touching the reference angle, but not the hypotenuse

A

hypotenuse

opp

osit

e

adjacent

a

b

c

A

B

C

sin cos tan

sin A° = opphyp cos A° =

adjhyp tan A° =

oppadj

sin A° = ac cos A° =

bc tan A° =

ab

S O H C A H T O A

Note: You cannot use trig ratios on the right angle

1. Find the sin R. Write your answer as a fraction.

sin R° = 1517

SOH – CAH – TOA

A

H

O

2. Find the cos A. Write your answer as a fraction.

cos A° = 1620

SOH – CAH – TOAA

H

O

3. Find the tan B. Write your answer as a fraction.

tan B° = 24.

10

SOH – CAH – TOA

A

H

O

4. Write the trigonometric ratio as a decimal to two decimal places.

a. sin 62° b. cos 25° c. tan 38°

0.88 0.91 0.78

5. Solve for x. Round to two decimal places.

1

x = 5 sin 24°

x = 2.03

sin 245

x a.

5. Solve for x. Round to two decimal places.

x

435tan

1

x tan35° = 4tan35° tan35°

x = 5.71

b.

Steps to solving with trig:

1.

2.

3.

4.

Label the sides with the reference angle

Choose a side to solve for

What side do you know and what side are you solving for?

Identify which trig ratio to use

cos 50° = a .

10

10 cos 50° = a

6.43 = a

A

H

6. Approximate the missing side length to two decimal places.

SOH – CAH – TOA

1

O

sin 42° = c .

7

7 sin 42° = c

4.68 = c

SOH – CAH – TOA

1A

HO

6. Approximate the missing side length to two decimal places.

m n

tan 39° = 25m

m tan 39° = 25

m = 30.87

SOH – CAH – TOA

1sin 39° =

25n

n sin 39° = 25

n = 39.73

1

tan 39° tan 39° sin 39° sin 39°

A

H

O

7. Approximate the missing side lengths to two decimal places.

t u

sin 51° = t .

32

32 sin 51° = t

24.87 = t

SOH – CAH – TOA

1cos 51° =

u .

32

32 cos 51° = u

20.14 = u

1

A

H

O

7. Approximate the missing side lengths to two decimal places.

a b

tan 57° = 14 a

a tan 57° = 14

SOH – CAH – TOA

1

tan 57° tan 57°

a = 9.09

sin 57° = 14 b

b sin 57° = 14

1

sin 57° sin 57°

b = 16.69

A

H

O

7. Approximate the missing side lengths to two decimal places.

m n

cos 31° = 79m

m cos 31° = 79

SOH – CAH – TOA

1

cos 31° cos 31°

m = 92.16

tan 31° = n .

79

79 tan 31° = n

1

n = 47.47

A

H

O

7. Approximate the missing side lengths to two decimal places.