# How to Find Missing Sides and Angles of a Right Triangle? (+FREE Worksheet!)

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

## Related Topics

- How to Evaluate Trigonometric Function
- How to Solve Angles and Angle Measure
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- How to Solve Trig Ratios of General Angles

## 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:**

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

**AC**\(=\) \( 0.70710 \) \(×\) \( 8 \) \( \cong 5.7 \) → **AC**\(=5.7\)

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

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

**Solution**:

\(sin\) \(θ=\frac{opposite}{hypotenuse}\). \(sin\) \(40^\circ=\frac{AC}{6}→6 ×\) \(sin\) \(40^\circ=AC\),**now use a calculator to find** \(sin\) \(40^\circ\). \(sin\) \(40^\circ\cong 0.642\)

**AC**\(=\) \( 0.642 \) \(×\) \(6 \) \( \cong 3.9 \) → **AC**\(= 3.9\)

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

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

## Answers

- \(\color{blue}{31.4}\)
- \(\color{blue}{7.0}\)
- \(\color{blue}{16.2}\)
- \(\color{blue}{31.1}\)

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