Right-triangle trigonometryFind an angle with trigonometry
Name: Date:
Find the angle marked x, to the nearest degree. Use a calculator.
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6 degrees
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.
If they get stuck
Finding 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 a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Finding a missing angle, step by step