Question

The angle of elevation of the top of a building
from foot of the tower is 30°
and the angle of elevation of the top of the tower from the root of the building
45° If tower is 30m high find the
height of
of the building​

Answer 1

Given:-

(From the foot for each)

The angel of elevation of top of building=30°

The angle of elevation of top of tower=45°

The height of tower=30m

To Find:-

The height of building=?

Solution:-

To calculate the height of building at, first we have to draw a figure then calculate calculate the height of building by setting up equation. As given in the question that The angle of elevation of the top of a building from foot of the tower is 30° and the angle of elevation of the top of the tower from the root of the building 45° If tower is 30m high.Now using trigonometry ratio to calculate the height of building Let's get ahead of this question.

Now as per the figures here:-]

∆ABC in which AB is the tower with angle 45°

∆BCD in which CD is the building with angle 30°

Let's calculation starting now:-]

In ∆ABC

=>Tan45°=Opposite side to angle c/adjecent side to angle c

=>Tan45°= AB/CB

=>1/1 = 30/CB

=>CB=30m--------(i)

In ∆BCD

=>Tan30°=CD/CB

=>1/√3 = CD/CB

=>CB=CD√3------(ii)

Here putting together eq (i) and (ii)

=>CB=CD√3

Putting the value of CB=30m here now:-]

=>30=CD√3

=>CD=30/√3

Here rationalize it now:-]

=>CD=30/√3

=>CD=30 × √3 / √3 × √3

=>CD=30√3/ √9

=>CD=30√3/3

=>CD=10√3m or 17.32m

Hence,

The height of building=10√3m or 17.32m

Answer 2

${\bf{Given\::}}$

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

• The angle of elevation of the top of the tower from the root of the building is 45°.

• Height of the tower is 30 m.

$\\ {\bf{To\: Find\::}}$

• The height of the building.

$\\ {\bf{Solution\::}}$

Let,

As shown in figure,

• Height of the building = PQ.

• Height of the tower = RS = 30 m.

• Angle of elevation of the top of a building from foot of the tower = $\rm{\angle{PRQ}}$ = 30°

• Angle of elevation of the top of the tower from the root of the building = $\rm{\angle{SQR}}$ = 45°

Since,

• Building & tower are perpendicular to the ground.

$\longrightarrow\:\bf{\angle{PQR}\:=\:\angle{SRQ}\:=\:90^{\circ}\:}$

Now,

In right angle ∆SQR,

➠ $\tt{\tan{45^{\circ}}\:=\:\dfrac{SR}{QR}\:}$

➠ $\tt{1\:=\:\dfrac{30}{QR}\:}$

➠ $\bf{QR\:=\:30\:cm}$

Again,

In right angle ∆PQR,

➠ $\tt{\tan{30^{\circ}}\:=\:\dfrac{PQ}{30}\:}$

➠ $\tt{\dfrac{1}{\sqrt{3}}\:=\:\dfrac{PQ}{30}\:}$

➠ $\tt{PQ\:=\:\dfrac{1}{\sqrt{3}}\times{30}\:}$

➠ $\bf\pink{PQ\:=\:10\sqrt{3}\:cm\:=\:17.32\:cm}$

∴ Height of the building is 17.32 cm.