Question

A kite flying at a height of 80 m above the ground is tied tightly to a nail on the top of a building of height 10 m, by thread. If the angle subtended by the thread with the building is 30 degree, find the length of the thread

Answer 1

GIVEN :

Height of the kite above ground =80m

Height of the building =10m

Angle subtended by thread =30°

To FIND :

Length of the thread

SOLUTION :

Refer to the attachment for better understanding.

So, on considering the figure the height of building be BC =10m.

And the height of the kite above the ground be AD =80m.

And, the length of the kite be AB.

Now,

AE =(AD-DE)=(80-10) [DE=BC]

AE = 70m.

As we know,

$\sin( \alpha ) = \frac{perpendicular}{hypotenuse}$

Hence,

$\sin(30) = \frac{AE} { AB}\\ \frac{1}{2} = \frac{70}{AB }\\ 70 \times 2 = AB = 140m$

Therefore, the length of the thread is 140m.