A person of height 6ft. wants to pluck a fruit which is on a 26/3 ft. high tree. If the person is standing 8/√3 ft. away from the base of the tree, then at what angle should he throw a stone so that it hits the fruit ?

Height of person = CD = 6 ft

Height of tree = AB = $$\frac{26}{3}$$ ft

Distance between them = BD = $$\frac{8}{\sqrt{3}}$$ ft

To find : $$\angle$$ACE = $$\theta$$ = ?

Solution : AE = AB - BE = $$\frac{26}{3}$$ - 6

=> AE = $$\frac{8}{3} ft$$

and BD = CE = $$\frac{8}{\sqrt{3}}$$ ft

Now, in $$\triangle$$AEC

=> $$tan\theta$$ = $$\frac{AE}{CE}$$

=> $$tan\theta$$ = $$\frac{\frac{8}{3}}{\frac{8}{\sqrt{3}}}$$

=> $$tan\theta$$ = $$\frac{1}{\sqrt{3}}$$

=> $$\theta$$ = 30°