Objectives Find the sine, cosine, and tangent of an acute angle. Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems.

SOH-CAH-TOA opposite sin x = hypotenuse opposite tan x = adjacent cos x = hypotenuse

opposite SinX= hypotenuse ALWAYS an ANGLE!!!

s√3 √3 = cos 30 = 2s 2 √3 cos 30 = 2 Example 1: Write cos 30° as a fraction. Draw and label a 30º-60º-90º ∆. s√3 √3 = cos 30 = 2s 2 √3 cos 30 = 2

Example 2: Use a special right triangle to write tan 45° as a fraction. s 45° Draw and label a 45º-45º-90º ∆. s tan 45 = =1 s

Example 3: Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Be sure your calculator is in degree mode, not radian mode. Caution! sin 52°  0.79

Caution! Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

Example 4: Find the length. Round to the nearest hundredth. opp adj BC BC  38.07 ft

Example 5: Find the length. Round to the nearest hundredth. opp QR hyp 12.9(sin 63°) = QR 11.49 cm  QR

Example 6: Find the length. Round to the nearest hundredth. hyp FD adj FD  25.74 m