A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flag-staff of height $h$ . At a point on the plane, the angle of elevation of the bottom and top of the flag staff are $45°$ and $60°$ respectively. Find the value of $h$ .

$Tower with flag-staff, angles 45° and 60°$

Question

A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flag-staff of height

h

. At a point on the plane, the angle of elevation of the bottom and top of the flag staff are

45°

and

60°

respectively. Find the value of

h

.

$Tower with flag-staff, angles 45° and 60°$

[IMAGE_1]

Accepted Answer

Step 1: Tower CD of height 20m with flag-staff of height h, angles 45° and 60° from point on ground
Step 2: Let $AC$ be the tower and $CD$ be the flag-staff. $	an 45° = \frac{AC}{AB} \Rightarrow AC = AB = 20$ m
Step 3: $	an 60° = \frac{AC + h}{AB} \Rightarrow \sqrt{3} = \frac{20 + h}{20}$
Step 4: $\Rightarrow h = 20(\sqrt{3} - 1)$ m

Question

Solution