7.5 & 7.6 Apply the Sin-Cos-Tan Ratios

Side opposite the given angleSide opposite the right angleSide touching the given angle, but not the hypotenuse

Opposite side:Hypotenuse:Adjacent side:

abcABCsincostansin A = opphypcos A = adjhyptan A = oppadjsin A = accos A = bctan A = abSOHCAHTOA

Note:You cannot use trig ratios on the right angle

1. Find the sin R and sin S. Write your answer as a fraction.sin R = 1517sin S = 8 .17SOH CAH TOA

2. Find the cos A and cos B. Write your answer as a fraction.cos A = 1620cos B = 12.20SOH CAH TOA

3. Find the tan A and tan B. Write your answer as a fraction.tan A = 1024tan B = 24.10SOH CAH TOA

4. Write the trigonometric ratio as a decimal to two decimal places.a. sin 62 b. cos 25c. tan 38 0.880.910.78

5. Solve for x. Round to two decimal places.1x tan35 = 4tan35tan35x = 5.71

When solving for a triangle using trigonometry, ask yourself these questions:

1.

2.

3.

4.What acute angle do I know?What side do I know?What side am I solving for?What is the relationship between the angle I know and the two sides? (opp, adj, or hyp)

abcos 50 = a .1010 cos 50 = a6.43 = aAH6. Approximate the missing variables to two decimal places. SOH CAH TOA1sin 50 = b .1010 sin 50 = b7.66 = b1OH

cdsin 42 = c . 77 sin 42 = c4.68 = cOH6. Approximate the missing variables to two decimal places. SOH CAH TOA1cos 42 = d . 77 cos 42 = d5.20 = d1AH

mntan 39 = 25mm tan 39 = 25m = 30.87SOH CAH TOAOA17. Approximate the missing variables to two decimal places. OHsin 39 = 25nn sin 39 = 25n = 39.731tan 39 tan 39sin 39 sin 39

tusin 51 = t .3232 sin 51 = t24.87 = tOHSOH CAH TOA17. Approximate the missing variables to two decimal places. AHcos 51 = u .3232 cos 51 = u20.14 = u1

abtan 57 = 14 aa tan 57 = 14SOH CAH TOAOA17. Approximate the missing variables to two decimal places. OHtan 57 tan 57a = 9.09sin 57 = 14 bb sin 57 = 141sin 57 sin 57b = 16.69

7. Approximate the missing variables to two decimal places. mncos 31 = 79mm cos 31 = 79AHSOH CAH TOA1cos 31 cos 31m = 92.16OAtan 31 = n .7979 tan 31 = n1n = 47.47