Question

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

Answer 1

✬ Height = 10√3 m ✬

Step-by-step explanation:

Given:

• Angle of elevation of top of a building from foot of tower is 30°.
• Angle of elevation of top of tower from foot of building is 45°.
• Height of tower is 30 m.

To Find:

• What is the height of building ?

Solution: Let AB be the tower and CD be a building of height 30 m and x m respectively and the distance between these two be y m.

[ In ∆ABC , using tanθ ]

★ tanθ = Perpendicular/Base ★

• Perpendicular = AB

• Base = BC

$\implies{\rm }$ tan45° = AB/BC

$\implies{\rm }$ 1 = 30/y

$\implies{\rm }$ y = 30

[ Now in ∆DBC , using tanθ ]

• Perpendicular = DC

• Base = BC

$\implies{\rm }$ tan30° = DC/BC

$\implies{\rm }$ 1/√3 = x/y

$\implies{\rm }$ 1/√3 = x/30

$\implies{\rm }$ 30 = √3 × x

$\implies{\rm }$ 30/√3 = x

➮ Let's rationalise the denominator

➮ 30/√3 × √3/√3

➮ 30√3/3

➮ 10√3 m

Hence, the height of building is 10√3 m.

Answer 2

Step-by-step explanation:

Given :

CD = 30 m Of Tower

Find :

Height Of The Building

Solution :

In ∆ BCD

tan 45° = CD / BC

1 = 30m / BC

BC = 30 m

Now In ∆ ABC

tan 30° = AB / BC

BC / √3 = AB

AB = 30√3

Remark ; Find Root Square 30 √3 So Convert

10 √3

AB = 10√3 m

Height Of The Building Is 10√3 m

Some Important Formula To Trigonometry

Sin teta = Perpendicular / Height

Cos teta = Base / Height

tan teta = Perpendicular / Base

Cose teta = Height / Perpendicular

Sec teta = Height / Base

Cot teta = Base / Perpendicular