Unit 7 Lesson 4 Apply the SinCosTan Ratios

Unit 7 Lesson 4 – Apply the Sin-Cos-Tan Ratios

Side touching the reference angle, but not the hypotenuse se nu Adjacent side: te Side opposite the reference angle po Opposite side: hy Side opposite the right angle opposite Hypotenuse: adjacent A

B a c C b A sin cos opp sin A° = hyp a sin A° = c adj cos A° = hyp b cos A° = c S O H C A tan H opp tan A° = adj a tan A° = b T O Note: You cannot use trig ratios on the right angle A

1. Find the sin R. Write your answer as a fraction. SOH – CAH – TOA H A O 15 sin R° = 17

2. Find the cos A. Write your answer as a fraction. SOH – CAH – TOA A 16 cos A° = 20 O H

3. Find the tan B. Write your answer as a fraction. SOH – CAH – TOA O A H 24 tan B° = 10 .

4. Write the trigonometric ratio as a decimal to two decimal places. a. sin 62° 0. 88 b. cos 25° 0. 91 c. tan 38° 0. 78

5. Solve for x. Round to two decimal places. a. 1 x = 5 sin 24° x = 2. 03

5. Solve for x. Round to two decimal places. b. 1 x tan 35° = 4 tan 35° x = 5. 71

Steps to solving with trig: 1. Label the sides with the reference angle 2. Choose a side to solve for 3. What side do you know and what side are you solving for? 4. Identify which trig ratio to use

6. Approximate the missing side length to two decimal places. SOH – CAH – TOA H a cos 50° = 10 1 . A O 10 cos 50° = a 6. 43 = a

6. Approximate the missing side length to two decimal places. SOH – CAH – TOA H O A c sin 42° = 7 1 . 7 sin 42° = c 4. 68 = c

7. Approximate the missing side lengths to two decimal places. A SOH – CAH – TOA O m H 25 tan 39° = m 1 m tan 39° = 25 tan 39° m = 30. 87 n 25 sin 39° = n 1 n sin 39° = 25 sin 39° n = 39. 73

7. Approximate the missing side lengths to two decimal places. H O SOH – CAH – TOA A t u t sin 51° = 32 1 u cos 51° = 32 1 32 sin 51° = t 32 cos 51° = u . 24. 87 = t . 20. 14 = u

7. Approximate the missing side lengths to two decimal places. H A SOH – CAH – TOA a O b 14 tan 57° = a 1 14 sin 57° = b 1 a tan 57° = 14 b sin 57° = 14 tan 57° sin 57° a = 9. 09 b = 16. 69

7. Approximate the missing side lengths to two decimal places. H A SOH – CAH – TOA m O cos 31° = 79 m 1 n tan 31° = n 79 1 . m cos 31° = 79 79 tan 31° = n cos 31° n = 47. 47 m = 92. 16