Question

A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The incli nation of the string with the ground is 60°. Find the length of the string assuming that there is no s lack in the string.​

Answer 1

$\huge\color{black}\boxed{\colorbox{cyan}{Question:-}}$

A kite is flying at a height of 60m 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°. Find the length of the string assuming that there is no s lack in the string.

$\huge\color{black}\boxed{\colorbox{cyan}{Answer}}\downarrow$

$ \blue{ \implies} $ 40√3 metre

† Step By Step Answer

Given That,

Height at which Kite is flying = 60 metre

Hence, AB = 60 m

Also, inclination of the string with the ground = 60°

Hence, ∠ACB = 60°

We have to find the length of the string, i.e., AC

Here, AB is perpendicular to ground

So, ∠ABC = 90°

In right triangle ABC,

sin C = Side opposite to angle C ÷ Hypotenuse

sin C = AB ÷ AC

sin 60° = 60 ÷ AC

√3 ÷ 2 = 60 ÷ AC

AC = 2 ÷ √3 × 60

AC = 120 ÷ √3

Multiplying √3 in both numerator and denominator

AC = 120 ÷ √3 × √3 ÷ √3

AC = 120√3 ÷ √3

AC = 40√3m

Hence, length of the string = AC = 40√3 metre

Answer 2

Answer:

40√3

Step-by-step explanation:

In ∆ABC

sin60 = P/H

= AB/AC

sin60 = √3/2

= √3/2 = 60m/hypotenuse

=√3hypotenuse=120

hypotenuse= 120/√3

= 40√3