Question 141
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
Solution
$$tan 30 = \frac{AB}{BC}$$ =$$ \frac{1}{\sqrt{3}}$$
$$cos 30 = \frac{BC}{AC} = \frac{sqrt{3}}{2}$$
Height of the tree = $$AB + AC$$
$$AB= BC \times \frac{1}{\sqrt{3}}$$
$$AB= 30 \times \frac{1}{\sqrt{3}} = \frac{30}{\sqrt{3}}$$
$$AC = \frac {2 \times BC}{\sqrt{3}} =\frac {2 \times 30}{\sqrt{3}}$$
$$AB+AC = \frac{30}{\sqrt{3}} + \frac {60}{\sqrt{3}} = 30\sqrt{3}$$
Hence Option B is the correct answer.
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