Question

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

Answer 1

Answer: 140m

Step-by-step explanation:

Answer 2

Answer:

140 m

Step-by-step explanation:

Figure attached.

Given Height of the building AD=10 m

Height of the kite from ground BC = 80 m

therefore, Height of the kite from the top of the building = (80-10)=70 m

The angle between the thread and building θ = 30°

Consider the length of the thread DC = x m

We know that

For a right triangle. If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.

In this figure DEC is a right angle triangle

$sin\theta=\frac{CE}{DC}\\\\sin30^{\circ}=\frac{70}{x}\\\\\frac{1}{2}=\frac{70}{x}\\\\x=70\times2=140$

Therefore the length of the thread is 140 m