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# How does SOHCAHTOA help us find side lengths?

After you are comfortable writing sine,cosine, tangent ratios, you might want to use sohcahtoa to find the sides of a right triangle. That is exactly the topic that this page focuses on.

### Practice Problems

Directions: Use sohcahtoa to find the given side length.

Example of finding Side Length
How to use sine,cosine,tangent to determine side X in the triangle below
 Step 1) Based on your givens and unknowns, determine which sohcahtoa ratio to use Since we know the 67 angle, its adjacent side length and we want to know length of the opposite side, we should use tangent Step 2) Set up an equation based on the ratio you chose in the step 1 $tan(67) = \frac{opposite}{adjacent}$ $tan(67) = \frac{x}{14}$ Step 3) Cross multiply and solve the equation for the side length. $tan(67) = \frac{x}{14}$ $14\times tan(67) = x$ $x \approx 32.98$
Problem 1) Use sine,cosine or tangent to find the value of side x in the triangle below.
 Step 1

Problem 2) Use sine,cosine or tangent to find the length of side k in the triangle below.
 Step 1

Problem 3) Use SOHCAHTOA to find x in the triangle on the left?

Problem 4) Use SOHCAHTOA to find  Y in the triangle on the left.

What are two distinct ways that you can find x in the triangle on the left?