Question

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

• A. $7 \sqrt{3}$
• B. $\frac{2}{3} \sqrt{21}$
• C. $\frac{3}{2} \sqrt{21}$
• D. $2 \sqrt{21}$

Answer 1

Answer: (B)

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

Answer 2

$BD = h \cot 30^{\circ} = h \sqrt{3}$
So, $7^2 + 5^2 = 2(h \sqrt{3})^2 + 3^2)$
$\Rightarrow \; 37 = 3h^2 + 9$
$\Rightarrow \; 3h^2 = 28$
$\Rightarrow \; h = \sqrt{\frac{28}{3}} = \frac{2}{3} \sqrt{21}$