Q7 of 61 Page 215

A lamp–post stands at the centre of a circular park. Let P and Q be two points on the boundary such that PQ subtends an angle 90° at the foot of the lamp–post and the angle of elevation of the top of the lamp post from P is 30°. If PQ = 30 m, then find the height of the lamp post.


Given that PQ = 30m and ∠POQ = 90°


Let O be the centre of the park and OR be the lamp post and P and Q be two points on the boundary of the circular park.


In a right triangle OPQ,


OP = OQ = radius.


⇒ ∠OPQ = ∠OQP = 45° (∵ POQ = 90°)


We know,





Multiplying and dividing ihe fraction by √2,we get–



= 15 √2


And, in triangle RPO,






Multiplying and dividing the fraction by √6, we get–




⇒ OR = 5√6


∴ the height of the lamp post is 5√6 m


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