Consider a triangular plot $ A B C $ with sides $ A B=7 m, B C=5 m $ and $ C A=6 m . $ A vertical lamp-post at the mid-point $ D $ of $ A C $ subtends an angle $ 30^{\circ} $ at $ B $. The height (in $ m $ ) of the lamp-post is:

Question

Consider a triangular plot $ A B C $ with sides $ A B=7 m, B C=5 m $ and $ C A=6 m . $ A vertical lamp-post at the mid-point $ D $ of $ A C $ subtends an angle $ 30^{\circ} $ at $ B $. The height (in $ m $ ) of the lamp-post is:, $ 2 \sqrt{21} $, $ \frac{2}{3} \sqrt{21} $, $ \frac{3}{2} \sqrt{21} $, $ 7 \sqrt{3} $

MARKS App · Accepted Answer

The length of the median B D is given by B D = 1 2 2 B C 2 + B A 2 - A C 2 ⇒ B D = 1 2 2 25 + 49 - 36 ⇒ B D = 1 2 112 ⇒ B D = 4 7 2 = 2 7 m . Now, let D T be the tower of height h m and it subtends ∠ T B D = 30 ° at the vertex B . Then, in ∆ T D B we have tan ∠ T B D = T D B D ⇒ tan 30 ° = h 2 7 ⇒ 1 3 = h 2 7 ⇒ h = 2 7 3 ⇒ h = 2 3 21 m .

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