One flies a kite with a thread 180 meter long. If the thread of the kite makes an angle of 60° with the horizontal line, then the height of the kite from the ground (assuming thread to be in straight line) is

Solution

Given:
– The length of the kite’s thread is 180 meters.
– The angle between the thread and the horizontal line is \(60^\circ\).

We can use trigonometry to find the height of the kite from the ground. The height (\(h\)) can be found using the sine function:

\[ \sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}} \]

In this case, the opposite side is the height of the kite (\(h\)), and the hypotenuse is the length of the thread (180 meters):

\[ \sin 60^\circ = \frac{h}{180} \]

We know that \(\sin 60^\circ = \frac{\sqrt{3}}{2}\), so:

\[ \frac{\sqrt{3}}{2} = \frac{h}{180} \]

Solving for \(h\):

\[ h = 180 \times \frac{\sqrt{3}}{2} \]
\[ h = 90\sqrt{3} \]

The height of the kite from the ground is \(90\sqrt{3}\) meters.