UPSC One
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2023 · Q99

The angles of elevation of the top of a tower from the top and bottom of a 10 metres tall building are 30º and 45º respectively. Approximately what is the height of the tower in metres from the top of the building (given that √3 = 1.73)?

General Mental Ability, Quantitative Aptitude and StatisticsTime, work and measurement
  1. A10.65
  2. B13.41
  3. C13.65
  4. D15.41

Explanation

Let h be the tower's height above the 10 m building and d the horizontal distance. From the bottom, tan45 = (10+h)/d, so d = 10+h; from the top, tan30 = h/d, so h = (10+h)/1.73, giving h x 0.73 = 10, i.e. h = 13.65 m approximately. Hence C.