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.
Find Missing Sides and Angles of a Right Triangle: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Choose the modelUse a right triangle, the unit circle, or a transformed graph.
- Track unitsConvert degrees and radians when needed.
- Use identitiesReplace complicated trig expressions with equivalent simpler ones.
Worked examples
Right-triangle sine
- Sine is opposite over hypotenuse.
- Substitute 5 and 13.
- Leave the ratio simplified.
Unit-circle cosine
- At angle 0, the point is (1, 0).
- Cosine is the x-coordinate.
- Read the x-value.
Try one before moving on
Find Missing Sides and Angles of a Right Triangle: pop-up practice
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
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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