Question

the angle of elevation of top of a building from foot of Tower 30 degree and the angle of elevation of the top of a tower from the foot of building is 60 degree if the tower is a 15 metre high and find is the height of the building​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

The angle of elevation of the top of a building from the foot of a Tower is 30°.

The angle of elevation of the top of the tower from the foot of the building is 60°.

Here, the tower is larger than the building.

Note :- Please keep this concept in your mind that if the angle of elevation is larger then the object is larger than the other.

The Tower is 15 metres tall.

We need to find out the height of the building which will be obviously smaller than the tower.

We assume it as x.

We also assume the distance between the base of the two objects as y.

Now, let us solve it !!!

In △ ABC,

$\leadsto \dfrac{x}{y} = \tan(30)$

$\leadsto\dfrac{x}{y} = \dfrac{1}{ \sqrt{3} }$

$\leadsto y = \sqrt{3} x$

.........equation 1

In △ DCB,

$\leadsto\dfrac{15}{y} = \tan(60)$

$\leadsto \dfrac{15}{y} = \sqrt{3}$

$\leadsto y = \dfrac{15}{ \sqrt{3} }$

........equation 2

Now, both the equations have the left hand side as equal.

So, we will equate their right hand sides.

Therefore,

$\leadsto \sqrt{3} x = \dfrac{15}{ \sqrt{3} }$

$\leadsto 3x = 15$

$\leadsto x = 5 \: m$

So, the height of the building is 5 metres.

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