Consider a triangular plot ABC with sides AB | vedclass

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Question

(B) Let $D$ be the midpoint of $AC$. $BD$ is the median to side $AC$.Using Apollonius theorem or the formula for the length of a median:$BD = \frac{1}

Vedclass · Accepted Answer

$\frac{2}{3} \sqrt{21}$

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(B) Let $D$ be the midpoint of $AC$. $BD$ is the median to side $AC$.Using Apollonius theorem or the formula for the length of a median:$BD = \frac{1}{2} \sqrt{2(AB^2 + BC^2) - AC^2}$$BD = \frac{1}{2} \sqrt{2(7^2 + 5^2) - 6^2}$$BD = \frac{1}{2} \sqrt{2(49 + 25) - 36}$$BD = \frac{1}{2} \sqrt{2(74) - 36} = \frac{1}{2} \sqrt{148 - 36} = \frac{1}{2} \sqrt{112}$$BD = \frac{1}{2} 	imes 4 \sqrt{7} = 2 \sqrt{7} \ m$.Let $h$ be the height of the lamp-post at $D$. The lamp-post subtends an angle $30^o$ at $B$,so in the right-angled triangle formed by the lamp-post and the segment $BD$:$	an 30^o = \frac{h}{BD}$$\frac{1}{\sqrt{3}} = \frac{h}{2 \sqrt{7}}$$h = \frac{2 \sqrt{7}}{\sqrt{3}} = \frac{2 \sqrt{21}}{3} \ m$.

Consider a triangular plot $ABC$ with sides $AB = 7 \ m$,$BC = 5 \ m$,and $CA = 6 \ m$. $A$ vertical lamp-post at the midpoint $D$ of $AC$ subtends an angle $30^o$ at $B$. The height (in $m$) of the lamp-post is

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