Question

Karan us standing at some distance from a tree. The height of the tree is 100m.if karan measure the angle of elevation to the top of the tree to be x such that sinx=1/2,find at what distance karan is standing.

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Answer 1

Answer:

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Answer 2

The distance of karan from the tree=$100\sqrt 3$m

Step-by-step explanation:

Height of tree=100m

$sin\theta=\frac{1}{2}$

We know that

$sin\theta=\frac{perpendicular\;side}{Hypotenuse}$

Substitute the values

$\frac{100}{Hypotenuse}=sin\theta=\frac{1}{2}$

$Hypotenuse=2\times 100=200m$

Pythagoras theorem:

$(Hypotenuse)^2=(base)^2+(Perpendicular\;side)^2$

Substitute the values

$(200)^2=(100)^2+x^2$

$40000=10000+x^2$

$40000-10000=x^2$

$x^2=30000$

$x=\sqrt{3\times 100\times 100}=100\sqrt 3$

Hence, the distance of karan from the tree=$100\sqrt 3$m

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