A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Answers (1)

 

tan space 30 to the power of degree space equals space BC over AB
rightwards double arrow space space fraction numerator 1 over denominator square root of 3 end fraction equals straight x over 8
rightwards double arrow space space space straight x space equals space fraction numerator 8 over denominator square root of 3 end fraction equals fraction numerator 8 square root of 3 over denominator 3 end fraction
and space cos space 30 to the power of degree space equals space AB over AC
rightwards double arrow space space fraction numerator square root of 3 over denominator 2 end fraction space equals space 8 over AC
rightwards double arrow space space space AC space space equals space fraction numerator 16 over denominator square root of 3 end fraction

rightwards double arrow space space space space straight y space space space equals space fraction numerator 16 over denominator square root of 3 end fraction equals fraction numerator 16 square root of 3 over denominator 3 end fraction

Now height of the tree

equals space left parenthesis straight x space plus space straight y right parenthesis space space metres
equals open square brackets fraction numerator 8 square root of 3 over denominator 3 end fraction plus fraction numerator 16 square root of 3 over denominator 3 end fraction close square brackets space metres
equals space fraction numerator 24 square root of 3 over denominator 3 end fraction space metres
equals 8 square root of 3 space metres

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