How to Find Missing Sides and Angles of a Right Triangle? (+FREE Worksheet!)
How to find missing sides and angles of a right triangle, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.
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^circcong 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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