The distance between two pillars is 120 metres. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is (Use: √3 = 1.732)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 103.92
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Application |
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In the figure:
BD = 120 and BO = OD = 120/2 = 60 Let AB = h and CD = 3h In triangle ABO: tanX = AB/BO ⇒ tanX = h/60 ……… (1) And In triangle COD: tan (90 – X) = CD/OD ⇒ cotX = 3h/60 ……. (2) From equations (1) and (2): tanX cotX = (h/60) × (3h/60) ⇒ 1 = 3h2/(60 × 60) ⇒ h2 = (60 × 60)/3 = 1200 ⇒ h = 20√3 m Hence, Length of taller pillar CD = 3 × 20√3 = 60 × 1.732 = 103.92 meters |
