$A$ 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

$A$ tower stands vertically on the ground. From a point on the ground,which is $15\, m$ away from the foot of the tower,the angle of elevation of the top of the tower is found to be $60^{\circ}.$ Find the height of the tower. (in $m$)

From a point $P$ on the ground,the angle of elevation of the top of a $10 \, m$ tall building is $30^{\circ}$. $A$ flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from $P$ is $45^{\circ}$. Find the length of the flagstaff and the distance of the building from the point $P$. (You may take $\sqrt{3} = 1.732$)

Difficult
View Solution

$A$ straight highway leads to the foot of a tower. $A$ man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$,which is approaching the foot of the tower with a uniform speed. Six seconds later,the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point (in $seconds$).

Difficult
View Solution

The angle of elevation of the top of a tower from a point on the ground,which is $30\, m$ away from the foot of the tower,is $30^{\circ}$. Find the height of the tower.

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 $m$)

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