Question

the angle of elevation of a top of tower from point A on the ground is 30 degree. on moving a distance of 20m towards the foot of the tower to a point B the angle of elevation increases to 60 degree. find the height of the tower and distance of the tower from point A

Answer 1

In the fig., CD is the tower.

Here, ΔABD is an isosceles triangle.

The ratio of sides of a 30°, 30°, 120° triangle is 1:1:√3.

∴ In ΔABD, 1:1:√3 = 20:20:20√3. (Given that AB = 20 m)

∴ BD = 20 m and AD = 20√3 m.

The ratio of sides of a 30°, 60°, 90° triangle is 1:√3:2.

∴ In ΔBCD, 1:√3:2 = 10:10√3:20 (Found that BD = 20 m)

∴ BC = 10 m and CD = 10√3 m.

Height of the tower is 10√3 m.

AC = AB + BC = 20 + 10 = 30 m

Distance from point A to the foot of the tower is 30 m.

That's all! There's no need to take trigonometrical equations like sin, cos and tan!

Thank you. Have a nice day.

#adithyasajeevan

Answer 2

tan teeta =opposite side/adjacent side

tan30=CD/AC

1/root3=CD/20
root3CD=20
CD=20/root3
CD=11.54
therefore.. height of the tower=11.54
hope this helps you....