Question

the angle of elevation off the top of a building from the foot of a tower is 30 degree and the angle of elevation of the top of the tower from the foot of the building is 60 degree. if the building is 50 metre height find the height of the tower​

Answer 1

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,

.........equation 1

In △ DCB,

........equation 2

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

So, we will equate their right hand sides.

Therefore,

So, the height of the building is 5 metres.

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Answer 2

Answer:

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

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

Height of the tower is 50 m.

Let the height of the building be h.

Step-by-step explanation:

$\sf In \: \Delta BDC$

$:\implies \sf tan \: \theta = \dfrac{Perpendicular}{Base}$

$:\implies \sf tan \: 60^{\circ} = \dfrac{CD}{BD}$

$:\implies \sf \sqrt{3} = \dfrac{50}{BD}$

$:\implies \sf BD = \dfrac{50}{ \sqrt{3} } \: m$

___________________

$\sf In \: \Delta ABD,$

$\dashrightarrow\:\: \sf tan \: 30 ^{\circ} = \dfrac{AB}{BD}$

$\dashrightarrow\:\: \sf \dfrac{1}{ \sqrt{3} } = \dfrac{AB}{BD}$

$\dashrightarrow\:\: \sf \dfrac{1}{ \sqrt{3} } = \dfrac{h}{ \dfrac{50}{ \sqrt{3} } }$

$\dashrightarrow\:\: \sf h = \dfrac{ 50 }{ \sqrt{3} \times \sqrt{3} }$

$\dashrightarrow\:\: \underline{ \boxed{\sf Height= \dfrac{50}{3} \: m }}$

$\therefore\:\underline{\textsf{Height of the building is \textbf{50/3 meter}}}.$