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.

Answer 1

Step-by-step explanation:

height=100m

base=x say

From given

sinx=1/2.

sinx=sin30°

x=30°

now,

tan30°=perp./base

1/√3=100/x

x=100√3

x=100*1.732

x=173.2 m

therefore,

Ram is standing at a distance of 173.2 m from the tree

Answer 2

Karan is standing at 173.21 meter away from the tree.

Step-by-step explanation:

As shown in the figure attached,

In the ΔABC,

Side AB represents the tree of height 100 m.

Karan measures the angle A [angle of elevation] from the point C = x°

It is given that sinx = $\frac{1}{2}$

Since $sinx=\frac{AB}{AC}$

$\frac{1}{2}=\frac{100}{AC}$

AC = 200 m

By Pythagoras theorem,

AC² = AB² + BC²

BC² = AC² - AB²

BC² = (200)² - (100)²

BC = $\sqrt{40000-10000}$

     = 100√3 meter

BC = 173.21 meter

Therefore, Karan is standing at 173.21 m from the tree.

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