Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m.

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 30o at B. The height (in m) of the lamp-post is -

Accepted Answer

BD = hcot30o = h$$\sqrt 3 $$

So, 72 + 52 = 2(h$$\sqrt 3 $$)2 + 32)

$$ \Rightarrow $$  37 = 3h2 + 9

$$ \Rightarrow $$  3h2 = 28

$$ \Rightarrow $$  h = $$\sqrt {{{28} \over 3}}  = {2 \over 3}\sqrt {21} $$

Solutions · 1