Question

A plan tree 90 ft high, is broken by the wind and its upper part meet the ground at an angle of ${30}^{\circ }$. Find the distance of the point where the top of the tree meets the ground, from its root:

• A. 43.69 ft
• B. 51.96 ft
• C. 60 ft
• D. 30 ft

Answer 1

The correct option is B 51.96 ft

Let the height from the ground (where the root is) at which the tree breaks be 'x' ft and let the distance between the root and the point at which the top of the tree hits the ground having been cut be 'd' ft.
Then,
Sin 30 = $\frac{x}{90-x}$
x = 30 ft.
cos 30 = $\frac{d}{60}$
d = 30 $\sqrt{3}$
d = 51.96 ft.