Question

The Angle of Depression of the top and bottom of 20m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

A) 20,10√3
B) 30,5√3
C) 20,10
D) 30,10√3

Answer 1

Answer:

Option D

Step-by-step explanation:

Keys:-

Red line- Multi-storage building

Blue line-20m tall building

Green Line- Distance between two buildings

Angle made between small black line and up green line is 30°

Angle made between big black line and down green line is 60°

In ΔABC,

1/√3 =h/x

x=√3*h

In ΔADE,

√3=(20+h)/√3*h

√3 * √3 h =20+h

3h=20+h

3h-h=20

2h=20

h=10 meters.

∴Length of multi-storage building

= h+20

=10+20

=30 meters.

Now,

Distance x (or) Length of DE=√3*h

=√3*10

Hence, Option D is your required answer..