Question

A flag-staff stands at the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is ${60}^o$ and from the same point, the angle of elevation of the top of the tower is ${45}^o$. Find the height of the flag-staff.

• A. $2.66m$
• B. $3.66m$
• C. $5.66m$
• D. none of these

Answer 1

The correct option is B $3.66m$

Based on the given information, we can draw the figure shown above.

Let BC be the height of the tower and DC be the height of the flag-staff.

In right triangle ABC,

$AB=BC\cot {45}^o$

$AB=5m$ .........(1)

In right triangle ABD,

$AB=BD\cot {60}^o$

$AB=(BC+CD)\cot {60}^o$

$AB=(5+CD)\frac{1}{\sqrt{3}}$ ......(2)

Equating 1 and 2, we get,

$(5+CD)\frac{1}{\sqrt{3}}=5$

$CD=5\sqrt{3}-5=5\times 0.732=3.66m$

Therefore, the height of the flagstaff is $3.66m$.