A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground . The distance from the foot of the tree to the point , where the top touches the ground is 10 m. Find the total height of the tree?

(AB+BC) = $$h$$ is the whole height of the tree, the tree breaks down from point A, BC = 10 m

In $$\triangle$$ ABC,

=> $$tan(30^\circ)=\frac{AB}{BC}$$

=> $$\frac{1}{\sqrt{3}}=\frac{AB}{10}$$

=> $$AB=\frac{10}{\sqrt{3}}$$ m ---------(i)

Again, in $$\triangle$$ ABC,

=> $$cos(30^\circ)=\frac{BC}{AC}$$

=> $$\frac{\sqrt{3}}{2}=\frac{10}{AC}$$

=> $$AC=\frac{20}{\sqrt{3}}$$ m ----------(ii)

Adding equations (i) and (ii),

=> $$AB+AC=\frac{10}{\sqrt{3}}+\frac{20}{\sqrt{3}}$$

=> $$h=\frac{30}{\sqrt{3}}=10\sqrt{3}$$ m

=> Ans - (A)