A tree 32 m tall broke due to a gale and its top fell at a distance of 16 m, from its foot. At what height above the ground did the tree break?

Open in App

Solution

Let the tree break at point P, which is at a height of x m from the ground. Suppose the top of the tree touches the ground at point F, which is at a distance of 16 m from the foot, B.

ΔPBF is a right-angled triangle. Applying Pythagoras theorem in right ΔPBF, we have:

Hence, the height at which the tree broke from the ground is 12 m.

Suggest Corrections

Similar questions

Due to strong wind, a part of tree $18 m$ high broke at a distance of $5 m$ from the ground, without separating from the main stem, top of the tree touched the ground. At what distance from the foot of the step did the top of the tree fall on the ground?

Q. A tree is broken by the wind but does not separate. If the point from where it breaks is 9 m above the ground and its top touches the ground at a distance of 12 m from its foot, find out the total height of the tree before it broke.

Q. When a eucalyptus tree is broken by strong wind its top strikes the ground at an angle of

30^{\circ}

to the ground and at a distance of

15

m from the foot. What is the height of the tree?

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree?

Q. A tree is broken from the height of 2.5 m of the ground at the distance of 6 m. What was the total height of tree before it broke

Join BYJU'S Learning Program