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QJEEM16Mae842: JEE Main 2016 Mathematics - Class 12 JEEM16Mae842 Solution: The angle of elevation of the top of a vertical tower from a…

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o. The angle of elevation of the top of the same tower from a point B, due south of A is 30o. If the distance between A and B is 542m, then the height of the tower (in metres), is :

Multiple Choice Options

  • A 363
  • B 54
  • C 543
  • D 108

Step-by-Step Verified Solution

JEE Main 2016 (Online) 10th April Morning Slot Mathematics - Height and Distance Question 30 English Explanation

Let the height of tower = h

In triangle PQA,

tan45o = hQA

⇒   h = QA

In triangle PQB,

tan300 = hBQ

⇒   BQ = 3h

In triangle BAQ

∠ QAB = 90o.

∴    QA2 + AB2 = QB2

⇒   h2 + (542)2 = (3h)2

⇒   2h2 = (542)2

⇒   2h = 542

⇒   h = 54 m

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