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Case study·Hard exam skill (4/5)·No calculator

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A surveyor observes the top of a tower from point PP at an angle of elevation 30∘30^\circ. She then walks 4040 m straight towards the tower to point QQ, where the angle of elevation becomes 60∘60^\circ.
Total: 5 marks

(a) If QQ is xx m from the tower, write the height in terms of xx using the observation at QQ. (1 mark)

(b) Write the height in terms of xx using the observation at PP. (1 mark)

(c) Find xx and the height of the tower. (3 marks)

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cbse-math-10.u5.t5-5.case.005

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