Question

The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is​

Answer 1

GIVEN :

• angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°

TO FIND :

• Find the height of tower

SOLUTION :

: $\implies$ Let tower be AB

: $\implies$ Let point C

: $\implies$ Distance of point C from foot of tower = 30m°

: $\implies$ since tower is vertical

: $\implies$ $\angle \: abc = 90 \degree$

: $\implies$ We need to find height of tower i.e AB

: $\implies$ In right angle ABC

: $\implies$ Tan C = side opposite angle C / side adjacent angle C

: $\implies$ TAN 30° = AB/ BC

: $\implies$ 1/√3 = AB/ 30

: $\implies$ 30/√3 = AB

: $\implies$ AB = 30/√3

Multiplying √3 is numerator and denominotor

: $\implies$ AB = 30/√3 × √3/√3

: $\implies$ AB = 30√3/ 3

: $\implies$ AB = 10√3

HENCE, THE HIGHT OF TOWER IS AB = 10 √3 m