Trig and Triangles

The angles of a triangle are labeled in clockwise order alphabetically. The sides are labeled by the opposite angles' lower case letters.

SOHCAHTOA is used to find missing angles and sides of a RIGHT triangle. Not wrong triangles.

sin(angle)=opposite/hypotenuse

cos(angle)=adjacent/hypotenuse

tan(angle)=opposite/adjacent

You cannot use the 90° angle in these formulas.

For word problems, the angle of elevation is from the ground up.

The angle of depression is from the highest point down.

Ex. 1

In triangle ABC, the angle of C = 90°, the angle of A = 37°, and side b = 25. Find c and a.

To find side c, you have to use an angle known that isn't 90°. You're going to take cos(37°) = 25/c. Cross multiply and plug into your calculator and you will get 31.303.

To find side a, you will take tan(37°) = a/25. Multiply everything by 25 and plug into your calculator and you will get 18.839.