1. 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.

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

3. opposite
SinX=
hypotenuse
ALWAYS an ANGLE!!!

4. 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

5. 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

6. 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

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

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

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

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