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

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

Missing Sides and Angles of a Right Triangle

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

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