Printable · GCSE Foundation · ages 14-16
Pythagoras’ theorem and trigonometric ratios worksheet — GCSE Foundation
Fifteen questions on "pythagoras’ theorem and trigonometric ratios" — DfE statement G20. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
part HigherNon-calculatoronly 8 unique questions available
Pythagoras’ theorem and trigonometric ratios worksheet — GCSE Foundation
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- 1.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.
- 2.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.
- 3.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.
- 4.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.
- 5.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.
- 6.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
- 7.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.
- 8.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.
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