Question

An observer $1.5$ m tall is $28.5$ m away from a tower and the angle of elevation from the eye of the observer is ${45}^o$. The height of the tower is:

• A. $27$ m
• B. $30$ m
• C. $28.5$ m
• D. None of these

Answer 1

The correct option is B $30$ m

Let $AB$ be the observer and $CD$ be the tower also refer the given figure :

$AC=BE=28.5m$

$AB$ =$CE$ =$1.5$ m,

Let $DE$=$h$ m

$\therefore$ From right angled $△BED$,

tan 45${}^o=\frac{DE}{BE}\Rightarrow 1=\frac{h}{28.5}$

$h=28.5$

$\therefore$ Height of tower $CD

$=h+1.5$

$=28.5+1.5$

$=30m$