Learn how to find the missing sides or angles of a right triangle when one length and one angle is provided.

## Step by step guide to finding missing sides and angles of a Right Triangle

- By using Sine, Cosine or Tangent, we can find an unknown side in a right triangle when we have one length, and one angle (apart from the right angle).
- Adjacent, Opposite and Hypotenuse, in a right triangle is shown below.
- Recall the three main trigonometric functions:

SOH – CAH – TOA, sin \(θ=\frac{opposite}{hypotenuse}\), Cos \(θ=\frac{adjacent}{hypotenuse}\), tan \(θ=\frac{opposite}{adjacent}\)

### Missing Sides and Angles of a Right Triangle – Example 1:

Find AC in the following triangle. Round answers to the nearest tenth.

**Solution:**

sin \((θ=\frac{opposite}{hypotenuse}\). sine \(45^\circ=\frac{AC}{8}→8 ×sin 45^\circ=AC\),**now use a calculator to find** sin \(45^\circ\). sin \(40^\circ=\frac{\sqrt{2}}{2}→AC \cong 0.70710\)

### Missing Sides and Angles of a Right Triangle – Example 2:

Find AC in the following triangle. Round answers to the nearest tenth.

**Solution**:

sine \(θ=\frac{opposite}{hypotenuse}\). sine \(40^\circ=\frac{AC}{6}→6 ×\) sine \(40^\circ=AC\),

now use a calculator to find sine \(40^\circ\). sine \(40^\circ\cong 0.642→AC \cong 3.9\)

## Exercises for Finding Missing Sides and Angles of a Right Triangle

### Find the missing side. Round answers to the nearest tenth.

## Answers

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- \(\color{blue}{7.0}\)
- \(\color{blue}{16.2}\)
- \(\color{blue}{31.1}\)