This worksheet applies Pythagoras' theorem and the trigonometric ratios to solve spatial problems in right-angled triangles, including real-world elevation and depression contexts. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Pythagoras' theorem: a²+b²=c² for a right-angled triangle with legs a, b and hypotenuse c.
- The trigonometric ratios (soh-cah-toa): sin(θ)=opposite/hypotenuse, cos(θ)=adjacent/hypotenuse, tan(θ)=opposite/adjacent.
- Given an angle and one side, trigonometry finds a missing side; given two sides, inverse trigonometry (sin⁻¹, cos⁻¹, tan⁻¹) finds a missing angle.
- Similar triangles have equal corresponding angles and proportional corresponding sides — the scale factor connects one triangle's dimensions to the other's.
- Angle of elevation (looking up) and angle of depression (looking down) are measured from the horizontal, and are used to solve real-world height/distance problems.
What your child will practise:
- Applying Pythagoras' theorem to find a missing side of a right-angled triangle.
- Applying sine, cosine or tangent to find a missing side, given an angle and one other side.
- Applying inverse trigonometric ratios to find a missing angle, given two sides.
- Using a similar-triangle scale factor to find an unknown length.
- Solving real-world angle-of-elevation/depression problems, combining trigonometry with careful diagram interpretation.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
.webp)
.webp)
%20(1).webp)
