NumericalHard4 marks
An aeroplane at an altitude of 1500 metres, finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.
Topic: Heights and distances
Previous-year question practice database
Answer
Solution diagram
Exam answer
Altitude = 1500 m.
Let the horizontal distances of the nearer and farther ships from the point vertically below the aeroplane be x and y.
For angle 45°: tan45° = 1500/x 1 = 1500/x x = 1500 m.
For angle 30°: tan30° = 1500/y 1/√3 = 1500/y y = 1500√3 ≈ 2598.08 m.
Both ships are in the same direction, so the distance between them = y − x = 1500(√3−1) ≈ 1098.08 m.
Answer: ≈ 1098 m.
Explanation
Angles of depression equal the corresponding angles of elevation. Because both ships are on the same side, subtract their horizontal distances.
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