Subhas, a 3.15 m tall tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Subhas and the building. The tree is located at a distance of 7.5 m from Subhas and at a distance of 45 m from the building. Further, the eyes of Subhas, the top of the tree, and the top of the building fall in one line. Find the height (in m) from the ground at which Subhas' eyes are situated.
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 1.8.
Let XA = OB = PC = h
XP = XO + OP = 7.5 + 45 = 52.5 m
In ΔXPZ, tan θ = PZ/PX = (11.25 - h)/52.5 .....(1)
In ΔXOY, tan θ = OY/OX = (3.15 - h)/7.5 .....(2)
From equations (1) and (2),
(11.25 - h)/52.5 = (3.15 - h)/7.5
⇒ 11.25 - h = 22.05 - 7h
⇒ 6h = 10.8
⇒ h = 10.8/6 = 1.8 m