The ratios
sin α = 3/5, cos α = 4/5, tan α = 3/4: level 1 gives all three sides as whole numbers; level 2 needs Pythagoras for the third side first; level 3 gives one ratio and asks for the other two, with surds rationalised.
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Teaching guide: how to practise right-angled triangle trigonometry
In a right-angled triangle, the sine, cosine and tangent of an acute angle link its sides. This free trigonometry worksheet generator builds A4 worksheets with triangles drawn to scale to write the trigonometric ratios, find missing sides and angles with a calculator, solve right-angled triangles, find angles inside shapes and solve word problems with heights and angles of elevation and depression. For Grade 10, with an answer key that shows every step.
- For
- Middle & High 10th (age 15)
- Subject
- Mathematics › Geometry & Measurement
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Missing sides
Choose the ratio that links the known side and the one you want. First the unknown is on top (x = 12 × sin 35°), then on the bottom (x = 12 ÷ sin 35°), and finally both missing sides are found.
Missing angles
With two sides, the ratio and the inverse function: tan α = 7/12, α = tan⁻¹(7/12) ≈ 30°. The other acute angle is 90° minus it, and at level 3 the angles hide inside rectangles, isosceles triangles and trapeziums.
Solving the triangle
Two sides, or a side and an angle: pupils work out everything that is missing and fill in a table with the sides a, b, c and the angles A, B, C. The answer key always works from the given data, never from rounded answers.
Word problems
Ladders, shadows, towers, roofs and ziplines, and at the last level two-triangle problems: two angles of elevation from two points, a mast seen from both sides and the building opposite, with the equations solved step by step.
Rounding
You choose whether lengths are rounded to 1 or 2 decimal places and angles to the nearest degree, tenth or minute. No answer sits close to a half, so a calculator and the answer key agree.
Frequently asked questions about trigonometry worksheets
Which grade learns right-angled triangle trigonometry?
Grade 10 (Year 10 and 11 at GCSE): sine, cosine and tangent, missing sides and angles, solving right-angled triangles and problems with heights and distances. The levels of the worksheets follow that order.
What does SOH CAH TOA mean?
Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent. The reminder option prints the three ratios under the instruction of each exercise.
How are answers rounded?
Lengths to 1 or 2 decimal places and angles to the nearest degree, tenth of a degree or minute, as you choose, and the instruction says so. The answer key writes the ratios to 4 decimal places, and no answer sits close to a half.
Which calculator do pupils need?
A scientific calculator in degree mode (DEG), with sin, cos and tan and their inverses. The first exercise type works with fractions, so no calculator is needed there.
Are the triangles drawn to scale?
Yes. Each triangle is drawn with its real angle and the right-angle mark, and the labels are placed clear of the lines. In the word problems pupils make the sketch and the answer key draws it.
What is in the answer key?
Every step: the ratio used, the equation, the unknown rearranged, the ratio to 4 decimal places and the rounded answer; for triangles to solve, the completed table; and for two-triangle problems, the equations solved.
What other worksheets go well with these?
The Pythagoras' theorem worksheets, which use the same triangles, the area and perimeter worksheets and the map and scale drawing worksheets for distance problems. Find every resource under maths worksheets.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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