# The Angle of Elevation of the Top of a Tower from a Point a on the Ground is 30°. Moving a Distance of 20metres Towards the Foot of the Tower to a Point B the Angle of Elevation Increases to 60°. Find the Height of the Tower and the Distance of the Tower from the Point A. - Mathematics

The angle of elevation of the top of a tower from a point A on the ground is 30°. Moving a distance of 20metres towards the foot of the tower to a point B the angle of elevation increases to 60°. Find the height of the tower & the distance of the tower from the point A.

#### Solution

Let h be the height of the tower and the angle of elevation of the top of the tower from a point A on the ground is  30° and on moving with distance 20 m  towards the foot of tower on the point B is 60°.

Let AB = 20 and BC = x

Now we have to find the height of tower and distance of tower from point A.

So we use trigonometrical ratios.

In ΔDBC

=> tan D = (CD)/(BC)

=> tan 60^@ = (CD)/(BC)

=> sqrt3 = h/x

=> x = h/sqrt3

Again in Δ DAC

=> tan A = (CD)/(BC + BA)

=> tan 30^@ = h/(x + 20)

=> 1/sqrt3 = h/(x + 20)

=> x = sqrt3h - 20

=> h/sqrt3 + 20 = sqrt3h

=> h/sqrt3 - sqrt3h = -20

=> h - 3h = -20sqrt3

=> -2h = -20sqrt3

=> h = 10sqrt3

=> h = 17.32

=> x = (10sqrt3)/sqrt3

=> x = 10

So distance

=> AC = x + 20`

=> AC = 30

Hence the required height is 17.32 m and distance is 30 m

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 16 | Page 30