Question

Fill in the blanks
The angle of elevation of the top of a tower from a point $A$ on the ground is $\theta$ and that from $B$ is $\varphi$. If $AB=100$ metres and $AB$ is perpendicular to the line joining $A$ with the foot of the tower, then the height of the tower is ________________.
Given $\cot \theta =3/10$ and $\cot \varphi =1/2$.

Answer 1

$\alpha =\theta ,\beta =\varphi ,AB=100$ m.
It is given that $\cot \theta =\frac{3}{10}$ and $\cot \varphi =1/2$
$\therefore h=\frac{AB}{\sqrt{(}{\cot }^2\varphi -{\cot }^2\theta )}=\frac{100}{\sqrt{(\frac{1}{4}-\frac{9}{100})}}$
$=\frac{1000}{\sqrt{(25-9)}}=\frac{1000}{4}=250$ m.