A 150-meter-tall tower stands on level ground. From the top of the tower, two cyclists are seen on the same side, moving directly towards the tower in straight lines. Initially, the angles of depression to the two cyclists are 35° and 20°, respectively. After 6 minutes, the angles change to 60° and 40°, respectively. Assuming both cyclists maintain a constant speed, find the approximate initial distance between them.
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Correct answer: A
Explanation
Height of the tower = 150 m
Distance = 150 / tan θ
First cyclist -
Initial distance = 150 / tan 35° ≈ 214 m
After 6 minutes = 150 / tan 60° ≈ 87 m
Difference = 214 − 87 = 127 m
Second cyclist -
Initial distance = 150 / tan 20° ≈ 412 m
After 6 minutes = 150 / tan 40° ≈ 179 m
Difference = 412 − 179 = 233 m
Estimated initial distance = 412 − 214 ≈ 198 m