Question

The angles of elevation of top of a building of an organisation working for conservation of wild life, from two points at a distance of 4 m and 9 m from the base of the builiding and in the same straight line with it are complementary. Prove that the height of the building is 6 m Why do we need conserve wild life?

Answer 1

Let AB be the building .

Let C and D be the two points at the distances of A and B respectively from the base of the tower.

Then AC=a=9 m , AD=b=4 m .

Let $\angle ACB=\theta$ and $\angle ADB={90}^o-\theta$.

Let h be the height of the building .

In triangle CAB, we have

$tan\theta =\frac{AB}{AC}=\frac{h}{9}$ ..........................1

In triangle DAB we have,

$tan({90}^o-\theta )=\frac{AB}{AD}=\frac{h}{4}$

$cot\theta =\frac{h}{4}$ ......................2

From eq. `1 and 2 we have,

$tan\theta \times cot\theta =\frac{h^2}{36}$

$1=\frac{h^2}{36}$

$h^2=36$

$h=6m$

We need to conserve wildlife because they are the beauty of our nature.