Question

A surveyor measured the angle of elevation of a flat spire as from a point on horizontal ground. He moves 30m nearer to the flat and measures the angle of elevation as . Calculate the height of the spire to the nearest hundredth.

Answer 1

tan$\theta$ = $\frac{h-a}{d}$

d = 30 m

h = height of spire

$\theta$ = angle of elevation

a = height of surveyor

tan$\theta$ = $\frac{h-a}{30}$

30×tan$\theta$ = h - a

h = (30 × tan$\theta$ ) + a