# Solving for a side in right triangles with trigonometry

CCSS Math: HSG.SRT.C.8

Learn how to use trig functions to find an unknown side length in a right triangle.

We can use trig ratios to find unknown sides in right triangles.

### Let's look at an example.

Given $\triangle ABC$, find $AC$.

### Solution

**Step 1:**Determine which trigonometric ratio to use.

Let's focus on angle $\goldD B$ since that is the angle that is explicitly given in the diagram.

Note that we are given the length of the $\purpleC{\text{hypotenuse}}$, and we are asked to find the length of the side $\blueD{\text{opposite}}$ angle $\goldD B$. The trigonometric ratio that contains both of those sides is thesine.

**Step 2:**Create an equation using the trig ratio

*sine*and solve for the unknown side.