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Trigonometry Ratios Practice Solutions | Calculate Sin, Cos, Tan

Practice solving trigonometry problems involving sine, cosine, and tangent ratios. Find missing side lengths using SOH-CAH-TOA methods. Includes step-by-step solutions and decimal conversions.

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Trigonometry Ratios Practice Solutions | Calculate Sin, Cos, Tan

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

  2. Side opposite the right angle hypotenuse opposite Side opposite the reference angle A adjacent Side touching the reference angle, but not the hypotenuse

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

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

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

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

  7. 4. Write the trigonometric ratio as a decimal to two decimal places. a. sin 62° b. cos 25° c. tan 38° 0.78 0.88 0.91

  8. 5. Solve for x. Round to two decimal places. a. 1 x = 5  sin 24° 2.03 x=

  9. 5. Solve for x. Round to two decimal places. b. 1 x  tan35° = 4 tan35° tan35° 5.71 x =

  10. 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

  11. 6. Approximate the missing side length to two decimal places. SOH – CAH – TOA H a. 10 cos 50° = A 1 10  cos 50° = a O 6.43 = a

  12. 6. Approximate the missing side length to two decimal places. SOH – CAH – TOA H O c. 7 sin 42° = A 1 7  sin 42° = c 4.68 = c

  13. 7. Approximate the missing side lengths to two decimal places. SOH – CAH – TOA A O m n 25 m H 25 n tan 39° = sin 39° = 1 1 m tan 39° = 25 n sin 39° = 25 tan 39° tan 39° sin 39° sin 39° m = 30.87 n = 39.73

  14. 7. Approximate the missing side lengths to two decimal places. H SOH – CAH – TOA A O t u t. 32 u. 32 sin 51° = cos 51° = 1 1 32  sin 51° = t 32  cos 51° = u 24.87 = t 20.14 = u

  15. 7. Approximate the missing side lengths to two decimal places. H SOH – CAH – TOA A a b O 14 a 14 b tan 57° = sin 57° = 1 1 a tan 57° = 14 b sin 57° = 14 tan 57° tan 57° sin 57° sin 57° a = 9.09 b = 16.69

  16. 7. Approximate the missing side lengths to two decimal places. H SOH – CAH – TOA A m n O 79 m n . 79 cos 31° = tan 31° = 1 1 m cos 31° = 79 79  tan 31° = n cos 31° cos 31° n = 47.47 m = 92.16

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