NumericalHard4 marks
The angle of elevation from a point P of the top of a tower QR, 50 m high is 60° and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre.
Topic: Heights and distances
Previous-year question practice database
Answer
Solution diagram
Exam answer
QR = 50 m.
tan60° = 50/PQ PQ = 50/√3.
For tower PT: tan30° = PT/PQ 1/√3 = PT/(50/√3)
PT = 50/3 ≈ 16.67 m.
Nearest metre:
Answer: 17 m.
Explanation
Use tanθ=opposite/adjacent in the two right triangles sharing horizontal distance PQ.
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