A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at $ 60^{\circ} $ to the horizontal. Find the length of the string to the nearest metre.

Given:

A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at \( 60^{\circ} \) to the horizontal.

To do:

We have to find the length of the string to the nearest metre.

Solution:  

Let $AB$ be the height above ground and $AC$ be the length of the string of the kite.

From the figure,

$\mathrm{AB}=75 \mathrm{~m}, \angle \mathrm{ACB}=60^{\circ}$

Let the length of the string be $\mathrm{AC}=h \mathrm{~m}$

We know that,

$\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$

$=\frac{\text { AB }}{AC}$

$\Rightarrow \sin 60^{\circ}=\frac{75}{h}$

$\Rightarrow \frac{\sqrt3}{2}=\frac{75}{h}$

$\Rightarrow h=75 \times \frac{2}{\sqrt3} \mathrm{~m}$

$\Rightarrow h=\frac{150}{\sqrt3} \mathrm{~m}$

$\Rightarrow h=\frac{150\sqrt3}{(\sqrt3)^2} \mathrm{~m}$

$\Rightarrow h=\frac{150\times1.732}{3} \mathrm{~m}$

$\Rightarrow h=86.6 \mathrm{~m}$

Therefore, the length of the string to the nearest metre is $87 \mathrm{~m}$.    

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Updated on: 10-Oct-2022

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