Question

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.

Solution

Let BD be the tree broken at point C such that the broken part CD takes the position CA and strikes the ground at A. It is given that AB = 8 m and ∠BAC = 30°.
Let BC = x metres and CD = CA = y metres
In right triangle ABC, we have
$tan space 30 to the power of degree space equals space BC over AB rightwards double arrow space space fraction numerator 1 over denominator square root of 3 end fraction equals straight x over 8 rightwards double arrow space space space straight x space equals space fraction numerator 8 over denominator square root of 3 end fraction equals fraction numerator 8 square root of 3 over denominator 3 end fraction and space cos space 30 to the power of degree space equals space AB over AC rightwards double arrow space space fraction numerator square root of 3 over denominator 2 end fraction space equals space 8 over AC rightwards double arrow space space space AC space space equals space fraction numerator 16 over denominator square root of 3 end fraction$

$rightwards double arrow space space space space straight y space space space equals space fraction numerator 16 over denominator square root of 3 end fraction equals fraction numerator 16 square root of 3 over denominator 3 end fraction$
Now, height of the tree
$equals space left parenthesis straight x space plus space straight y right parenthesis space space metres equals open square brackets fraction numerator 8 square root of 3 over denominator 3 end fraction plus fraction numerator 16 square root of 3 over denominator 3 end fraction close square brackets space metres equals space fraction numerator 24 square root of 3 over denominator 3 end fraction space metres equals 8 square root of 3 space metres$
Hence, the height of the tree $equals space 8 square root of 3 space straight m.$

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Circles

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.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?

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For Daily Free Study Material Join wiredfaculty

Circles

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.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O1 and O2 of the object at A?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?