Two towers of equal height stand on either side of a 120 m wide road. From a point on the road between them, the angles of elevation of the tops are 30° and 60°. Find the height of the towers (in m).

Question

Accepted Answer

30 √3. Let height h, distance to first tower = x, to second = 120-x. tan60 = h/x and tan30 = h/120-x. So x = h√3, 120-x = h √3. Add: 120 = h√3 + h √3 = h(1+3)√3 = 4h√3 => h = 30 √3 m.

Two towers of equal height stand on either side of a 120 m wide road.
From a point on the road between them, the angles of elevation of the tops are 30° and 60°.
Find the height of the towers (in m).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Heights and Distances practice

Two towers of equal height stand on either side of a 120 m wide road.From a point on the road between them, the angles of elevation of the tops are 30° and 60°.Find the height of the towers (in m).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Heights and Distances practice

Two towers of equal height stand on either side of a 120 m wide road.
From a point on the road between them, the angles of elevation of the tops are 30° and 60°.
Find the height of the towers (in m).