Question

A kite is flying at a height of 75 metres from the level of ground attached to a string inclined at 60° to the
horizontal. Find the length of the string.​

Answer 1

This question test the concept of Trigonometry.

Recall the formula:

• $\sin \theta = \dfrac{\text{opposite}}{\text{hypothenuse}}$
• $\cos \theta = \dfrac{\text{adjacent}}{\text{hypothenuse}}$
• $\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

Given:

Height = 75 m

Angle inclined = 60°

Find the length of the string (which is the hypotenuse):

$\sin \theta = \dfrac{\text{opposite}}{\text{hypothenuse}}$

$\sin(60) = \dfrac{75}{\text{hypothenuse}}$

$\text{hypothenuse} = \dfrac{75}{\sin(60)}}$

$\text{hypothenuse} = 50\sqrt{3}$

Find the length of the string:

$\text{length } = 50\sqrt{3}$

$\text{length } = 86.6 \text{ m}$

Answer: The length of the string is 86.6 cm

Answer 2

$\huge \boxed{ \fcolorbox{cyan}{red}{Answer : }}$

$\sf{let \: AB - 75 - height \: of \: the \: pole}$

$\sf{ad \: be \: the \: wire}$

$\sf{traingle \:ABD}$

$\sf{ \sin(60) = \frac{AB}{AD} = \frac{ \sqrt{3} }{2} = \frac{75}{AD}}$

$\sf{ad = \frac{150}{ \sqrt{3}}}$

$\sf{ \frac{150}{1.73}}$