Question

From a certain spot, the top of a flagpole has an angle of elevation of 30°. After moving 10 m in a straight line towards the flagpole, the top has an angle of elevation of 50° . Find the height of the flagpole.
(Use sin 50° = 0.766, cos 50° = 0.643, tan 50° = 1.192)

Answer 1

Let the height of the flagpole be h.
Then,
$tan50°=\frac{h}{x}...\left(i\right)$
$tan30°=\frac{h}{x+10}...\left(ii\right)$

$\frac{1}{\sqrt{3}}=\frac{h}{x+10}\left(from\right(ii\left)\right)x+10=\sqrt{3}\times h...\left(iii\right)$

$1.192=\frac{h}{x}\left(from\right(i\left)\right)1.192x=h...\left(iv\right)$
$Substitute\left(iv\right)in\left(iii\right),thenx+10=\sqrt{3}\times 1.192x1.0646x=10x=\mathrm{9.39.}$

$Substitutethevalueofxin\left(iv\right),weget,1.192\times 9.39=hh=11.19$

Thus, the height of the flag pole is 11.19 m.