This worksheet applies Pythagoras' theorem and right-angled trigonometry to practical problems involving direction and angles of elevation and depression. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Pythagoras' theorem: in a right-angled triangle, a²+b²=c² (where c is the hypotenuse) — used to find a missing side when two others are known.
- soh cah toa: sin(θ)=opposite/hypotenuse, cos(θ)=adjacent/hypotenuse, tan(θ)=opposite/adjacent — used to find a missing side or angle when a right angle and one other angle (or two sides) are known.
- An angle of elevation is measured upward from the horizontal (e.g. looking up at a tower from the ground).
- An angle of depression is measured downward from the horizontal (e.g. looking down at a boat from a cliff top).
- The angle of elevation from point A to point B equals the angle of depression from point B to point A (alternate angles, since the horizontal lines at A and B are parallel).
What your child will practise:
- Applying Pythagoras' theorem to find a missing side of a right-angled triangle.
- Applying soh cah toa to find a missing side or a missing angle of a right-angled triangle.
- Seting up and solve a problem involving an angle of elevation or depression from a real-world description.
- Solving a two-triangle problem (e.g. two observers at different distances from the same object).
- Correctlying identify which trig ratio to use, based on which sides/angle are known and which is required.
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.
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