Question

Angle of elevation of the top of a tower from a point of on ground which is 30 m away from the foot of the tower is 30° height of the tower is

Answer 1

Answer:

Step-by-step explanation:

let the height =h

tan30°=h/30

1/root3=h/30

h=30/root3

h=10root3

Answer 2

✬ Height of Tower = 10√3 m ✬

Step-by-step explanation:

Given:

• Angle of elevation of top of tower is 30°.
• Distance of point from the foot of tower is 30 m.

To Find:

• What is the height of tower i.e AB ?

Solution: Let the tower be AB and the point which is 30 m away from foot of tower be C.

➯ Distance of point C from the foot of tower = 30 m

➯ So, BC = 30 m.

Since, the angle of elevation is 30° and the tower is vertical, therefore

➼ ∠ACB = 30° & ∠ABC = 90°.

Now, In right ∆ABC,

• tan C = Side opposite to angle C/ Side adjacent to angle C

$\implies{\rm }$ tan 30° = AB/BC

$\implies{\rm }$ 1/√3 = AB/30

$\implies{\rm }$ 30 = √3AB

$\implies{\rm }$ 30√3 = AB

• Rationalising the fraction •

$\implies{\rm }$ 30√3 $\times$ √3/√3 = AB

$\implies{\rm }$ 30√3/√9 = AB

$\implies{\rm }$ 30√3/3 = AB

$\implies{\rm }$ 10√3 = AB

Hence, the height of tower AB is 10√3m.