The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Sine, cosine, tangent – worksheets to print
Name the opposite side, the adjacent side and the hypotenuse in a right-angled triangle, work out sides and angles with sine, cosine and tangent, solve word problems about ramps, ladders and towers, and use the sine rule and the cosine rule in any triangle.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Sine, cosine, tangent: explained simply
In a right-angled triangle, the ratios of the sides depend only on the angles. With sine, cosine and tangent you use them to find missing sides and angles.
How to work it out
- The hypotenuse lies opposite the right angle and is the longest side. The opposite side lies opposite the angle α; the adjacent side touches α.
- sin α = opposite : hypotenuse, cos α = adjacent : hypotenuse, tan α = opposite : adjacent.
- Find an angle with the inverse key: sin α = 0.6 gives α = sin⁻¹(0.6) ≈ 37°. The calculator must be set to degrees (DEG).
An example, step by step
In triangle ABC, γ = 90°, α = 35° and c = 8 cm. Work out a.
- a lies opposite α, so it is the opposite side; c is the hypotenuse.
- sin 35° = a : 8 cm, so a = 8 cm · sin 35°.
- a ≈ 8 · 0.5736 ≈ 4.6 cm.
Understand other variations
The missing side is in the denominator
If a = 5 cm and α = 35° are given and c is missing: sin 35° = 5 cm : c, so c = 5 cm : sin 35° ≈ 8.7 cm.
Word problems
A ramp rises 0.5 m over a horizontal distance of 6 m. tan α = 0.5 : 6, so α = tan⁻¹(0.5 : 6) ≈ 5°.
Sine rule and cosine rule (grade 10)
In any triangle, a : sin α = b : sin β (sine rule) and a² = b² + c² − 2bc · cos α (cosine rule). Use the cosine rule when two sides and the angle between them, or all three sides, are given.
Your turn
γ = 90°, b = 4 cm, c = 5 cm. How big is α?
Show the answer and method
b is the side adjacent to α and c is the hypotenuse: cos α = 4 : 5 = 0.8, so α ≈ 37°.
Ready-made worksheets: Sine, cosine, tangent
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