NumericalHard3 marks
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships, Give your answer correct to the nearest whole number.
Topic: Heights and distances
Previous-year question practice database
Answer
Solution diagram
Exam answer
Height of lighthouse = 60 m.
For ship A: tan60° = 60/x x = 60/√3 = 20√3 ≈ 34.64 m.
For ship B: tan45° = 60/y y = 60 m.
The ships are on opposite sides.
Distance between ships = 34.64 + 60 = 94.64 m.
Answer: ≈ 94.6 m.
Explanation
Angles of depression equal the corresponding angles of elevation. Use tanθ = height/horizontal distance for each ship, then add the distances.
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