A tree is broken by the wind. If the top of the tree struck the ground at an angle of 30° and at a distance of 30 m from the root, then the height of the tree is ?->(Show Answer!)

1. A tree is broken by the wind. If the top of the tree struck the ground at an angle of 30° and at a distance of 30 m from the root, then the height of the tree is

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By: anil on 05 May 2019 01.59 am

$$tan 30 = frac{AB}{BC}$$ =$$ frac{1}{sqrt{3}}$$
$$cos 30 = frac{BC}{AC} = frac{sqrt{3}}{2}$$
Height of the tree = $$AB + AC$$
$$AB= BC imes frac{1}{sqrt{3}}$$
$$AB= 30 imes frac{1}{sqrt{3}} = frac{30}{sqrt{3}}$$
$$AC = frac {2 imes BC}{sqrt{3}} =frac {2 imes 30}{sqrt{3}}$$
$$AB+AC = frac{30}{sqrt{3}} + frac {60}{sqrt{3}} = 30sqrt{3}$$
Hence Option B is the correct answer.

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