Question

a flagstaff of height 10 stands in platform if the angles of elevation of top and bottom of flag staff are 60 degree and 30 degree from a point on the ground find the height of the platform

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Answer 1

SOLUTION:-

Given:

A flagstaff of height 10m stands in platform if the angles of elevation of top & bottom of flagstaff are 60° & 30° from a point on the ground.

To find:

The height of the platform.

Explanation:

Let the height of the platform be R m.

We have,

• Height of flagstaff,(AD)=10m
• A point on the ground,(BC)=x m

According to the question:

In right angled ∆BCD;

$tan \theta = \frac{Perpendicular}{Base}$

So,

$tan30 \degree = \frac{DC}{BC} \\ \\ \frac{1}{ \sqrt{3} } = \frac{R}{x} \\ \\ x =R \sqrt{3} ............(1)$

&

In right angled ∆ABC:

$tan60 \degree = \frac{AD + DC}{BC} \\ \\ \sqrt{3} = \frac{10 + R}{x} \\ \\ \sqrt{3} x = 10 + R \\ \\ x = \frac{10 + R}{ \sqrt{3} } .............(2)$

Now,

Comparing equation (1) & (2), we get;

$R \sqrt{3} = \frac{10 + R}{ \sqrt{3} } \\ \\ R \sqrt{3} \times \sqrt{3} = 10 + R \\ \\ 3R= 10 + R \\ \\ 3R - R = 10 \\ \\ 2R = 10 \\ \\ R = \frac{10}{2} \\ \\ R = 5m$

Thus,

The Height of the platform is 5m.