Right-triangle trigonometryFind an angle with trigonometry
Name: Date:
Find the angle marked x, to the nearest degree. Use a calculator.
1 degrees
2 degrees
3 degrees
4 degrees
5 degrees
6 degrees
- Free
- Grade 9
- Inverse trig, calculator, rounded
Finding a missing angle worksheets
When both legs — or a leg and the hypotenuse — of a right triangle are known, the angle is fixed, and the inverse ratios find it. These free printable worksheets give two sides and ask for the angle marked x.
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Ready to printFinding a missing angle
The answer key prints on a separate page.
What's on this sheet
Finding an angle runs a ratio backward. From the two known sides you still name sine, cosine or tangent by SOHCAHTOA, write the ratio as a fraction, and then reach for the inverse key — sin⁻¹, cos⁻¹ or tan⁻¹ — to turn that ratio into the angle. The figures are drawn to their true shape, so a student can eyeball whether the angle is nearer 30° or nearer 60° and catch a calculator slip before it is written down.
Why this sheet works
This is a calculator worksheet and prints for that reason: the inverse of a fraction is not something that sits on the page, and the answer is a rounded value. Each angle is asked to the nearest degree, and the answer key gives it. A student works this one with a calculator beside them, set to degrees.
How this one works
One question from this sheet, worked through a step at a time.
Find the angle: opposite 5, adjacent 13
tan x=5 ÷ 13
x=tan⁻¹(5 ÷ 13)
x=21°
- You know the two legs: the side opposite the angle is 5, and the side next to it (adjacent) is 13. Opposite over adjacent is the tangent.
- To undo the tangent, use inverse tangent (tan⁻¹ on the calculator): x = tan⁻¹(5 ÷ 13).
- That is 21° to the nearest degree.