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 opposite adjacent
a b c A B C sin cos tan sin A° = opp hyp cos A° = adj hyp tan A° = opp adj sin A° = acac cos A° = bcbc tan A° = abab SOHCAHTOA Note: You cannot use trig ratios on the right angle
1. Find the sin R. Write your answer as a fraction. sin R° = SOH – CAH – TOA A H O
2. Find the cos A. Write your answer as a fraction. cos A° = SOH – CAH – TOA A H O
3. Find the tan B. Write your answer as a fraction. tan B° = 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°
5. Solve for x. Round to two decimal places. 1 x = 5 sin 24° x =x = 2.03 a.
5. Solve for x. Round to two decimal places. 1 x tan35° = 4 tan35° x = 5.71 b.
Steps to solving with trig: 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 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 1 A H O 6. Approximate the missing side length to two decimal places.
mn tan 39° = 25 m m tan 39° = 25 m = SOH – CAH – TOA 1 sin 39° = 25 n n sin 39° = 25 n = tan 39° sin 39° A H O 7. Approximate the missing side lengths to two decimal places.
tu sin 51° = t sin 51° = t = t SOH – CAH – TOA 1 cos 51° = u cos 51° = u = u 1 A H O 7. Approximate the missing side lengths to two decimal places.
ab tan 57° = 14 a a tan 57° = 14 SOH – CAH – TOA 1 tan 57° a = 9.09 sin 57° = 14 b b sin 57° = 14 1 sin 57° b = A H O 7. Approximate the missing side lengths to two decimal places.
mn cos 31° = 79 m m cos 31° = 79 SOH – CAH – TOA 1 cos 31° m = tan 31° = n tan 31° = n 1 n = A H O 7. Approximate the missing side lengths to two decimal places.