# Ex.9.1 Q5 Some Applications of Trigonometry Solution - NCERT Maths Class 10

## Question

A kite is flying at a height of \(60\,\rm{m}\) above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is \(60^\circ\). Find the length of the string, assuming that there is no slack in the string.

## Text Solution

**What is Known?**

(i) Kite flying at a height \(= 60\,{\rm { m}}\)

(ii) Angle made by the string to the ground \(=60^\circ\)

**What is Unknown?**

Length of the string \(\)

**Reasoning:**

Let the height of the flying kite as \(AB\), length of the string as \(AC\) and the inclination of the string with the ground as \(\angle C\)

Trigonometric ratio involving \(AB, AC\) and \(\angle C\) is \(\sin \theta\)

**Steps:**

In \(\Delta ABC\),

\[\begin{align}\sin \,C &= \frac{{AB}}{{AC}}\\\sin \,{60^0} &= \frac{{60}}{{AC}}\\\frac{{\sqrt 3 }}{2} &= \frac{{60}}{{AC}}\\AC &= \frac{{60 \times 2}}{{\sqrt 3 }}\\&= \frac{{120}}{{\sqrt 3 }} \times \frac{{\sqrt 3 }}{{\sqrt 3 }}\\&= \frac{{120\sqrt 3 }}{3}\\&= {\rm{40}}\sqrt {\rm{3}} \,\end{align}\]

Length of the string \(AC =\) \(40 \sqrt{3} \mathrm{m}\)