$A$ kite is flying at a height of $60\, m$ 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.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
$(40\sqrt{3}\, m) $ Let $K$ be the position of the kite and $P$ be the point on the ground where the string is tied. Let $L$ be the point on the ground directly below the kite.
In the right-angled triangle $\triangle KLP$:
$KL = 60\, m$ (height of the kite)
$\angle KPL = 60^{\circ}$ (angle of inclination)
We need to find the length of the string,which is the hypotenuse $KP$.
Using the trigonometric ratio $\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$:
$\sin 60^{\circ} = \frac{KL}{KP}$
$\frac{\sqrt{3}}{2} = \frac{60}{KP}$
$KP = \frac{60 \times 2}{\sqrt{3}}$
$KP = \frac{120}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$
$KP = \frac{120\sqrt{3}}{3} = 40\sqrt{3}\, m$
Thus,the length of the string is $40\sqrt{3}\, m$ (approximately $69.28\, m$).

Explore More

Similar Questions

An observer $1.5\, m$ tall is $28.5\, m$ away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^{\circ}$. What is the height of the chimney? (in $m$)

$A$ $TV$ tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower,the angle of elevation of the top of the tower is $60^{\circ}$. From another point $20 \, m$ away from this point on the line joining this point to the foot of the tower,the angle of elevation of the top of the tower is $30^{\circ}$ (see figure). Find the height of the tower and the width of the canal.

Difficult
View Solution

$A$ statue,$1.6 \, m$ tall,stands on the top of a pedestal. From a point on the ground,the angle of elevation of the top of the statue is $60^{\circ}$ and from the same point the angle of elevation of the top of the pedestal is $45^{\circ}$. Find the height of the pedestal.

Difficult
View Solution

From the top of a $7 \,m$ high building,the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.

Difficult
View Solution

$A$ tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground,making an angle of $30^{\circ}$ with it. The distance between the foot of the tree and the point where the top touches the ground is $8\, m$. Find the height of the tree.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo