GATE CE 2019 Set 1 — Question 3
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
On a horizontal ground, the base of a straight ladder is away from the base of a vertical pole. The ladder makes an angle of to the horizontal. If the ladder is resting at a point located at one-fifth of the height of the pole from the bottom, the height of the pole is ________ meters.
Correct answer
(C) 30
Solution
Let the height of the pole be . The ladder rests at a height of from the bottom. The distance from the base of the pole to the base of the ladder is . The angle of the ladder with the horizontal is . In the right-angled triangle formed by the ladder, the pole, and the ground:Thus, the height of the pole is .
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