Question
The upper part of a tree broken over by the wind makes an angle of $${30^ \circ }$$ with the ground and the distance from the root to the point where the top of the tree touches the ground is $$10\,m;$$ what was the height of the tree
A.
$$8.66\,m$$
B.
$$15\,m$$
C.
$$17.32\,m$$
D.
$$25.98\,m$$
Answer :
$$17.32\,m$$
Solution :
Height of tree is
$$AB + AC = \frac{{20}}{{\sqrt 3 }} + \frac{{10}}{{\sqrt 3 }} = \frac{{30}}{{\sqrt 3 }} = 10\sqrt 3 = 17.32\,m$$
Height of tree is
$$AB + AC = \frac{{20}}{{\sqrt 3 }} + \frac{{10}}{{\sqrt 3 }} = \frac{{30}}{{\sqrt 3 }} = 10\sqrt 3 = 17.32\,m$$