# SOHCAHTOA (sine, cosine, & tangent)

Learn how to apply sine, cosine and tangent (SOHCAHTOA) in right triangles to solve for missing lengths in the triangle.

SOHCAHTOA
$sin\theta = \frac{opposite}{hypotenuse}$
$cos\theta = \frac{adjacent}{hypotenuse}$
$tan\theta = \frac{opposite}{adjacent}$

For example:
In a right triangle, one leg has a measure of 4 units and the opposite angle has a measure of 30 degrees. Determine the length of the hypotenuse.

Since the angle measure given is opposite of the side and the question asks to find the hypotenuse, sin can be used to find the missing length.
$sin\theta = \frac{opposite}{hypotenuse}$

Substitute the variables
$sin 30= \frac{4}{hypotenuse}$

Solve for sin 30
$0.5 = \frac{4}{x}$

Multiple x on both sides
$0.5x = \frac{4}{x}\times x$
$0.5x = 4$

Divide 0.5 on both sides to isolate x
$x = 8$
The hypotenuse is 8 units