Question

Due to wind a tree was broken and its head touches
the ground at angle of 60°. Find the ratio of its original
height to present height.
(A) 213 +3
(B) 273 - 3
(c) 2/3 + 3
(D) 213 – 3​

Answer 1

Answer:

The ratio is (2√3 + 3)/3

Step-by-step explanation:

Let ABC be the tree before it was broken

After breaking, the top of the tree C touches the ground at point C'

∠AC'B = 60°

Also, AB + BC = AB + BC'

In ΔAC'B

sin60° = AB/BC'

√3/2 = AB/BC'

or BC' = 2AB/√3

Original height of the tree = AB + BC'

                                           = AB + 2AB/√3

                                          = AB(√3 + 2)/√3

New height of the tree = AB

Ratio of the original height to the present height

= AB(√3 + 2)/√3/AB

= (√3 + 2)/√3

= (2√3 + 3)/3

Hope this helps.