Question

the upper part of tree broken by wind makes an angle of 45 with the ground and horizontal distance from the foot of the tree to the point where the top of tree touches the ground is 12 m, find the height of tree before it was broken ?

Answer 1

total length of tree is x+y

use cos45°= 12/y to find y.

use tan45°=x/12 to find x.

add x and y to get total length of tree before breaking

Answer 2

Let length of tree before windstorm is BD.

After windstorm the upper part of tree C falls from point C to point A on the ground

. Now, let CD = AC = h2 m AB = 10 m

Broken part makes an angle 60° from the ground.

So, ∠CAB = 60°

From right angled ∆ABC tan 60° = BC/AB ⇒ √3 = h1/10 ⇒ h1 = 10√3 and cos 60° = AB/AC ⇒ 1/2 = 10/h2 ⇒ h2 = 10 × 2 = 20 m

Hence, total length of tree BD = BC + CD = h1 + h1

= 10√3 + 20

= 10 × 1.732 + 20

= 17.32 + 20

= 37.32 m

Hence, height of the tree 37.32 m.