question_answer

One flies a kites with a thread 150 m long. If the thread of the kite makes an angle of \[60{}^\circ \] with the horizontal line, then the height of the kite from the ground (assuming the thread to be in a straight line) is?

A)  50 m

B)  \[75\sqrt{3}\,m\]

C) \[25\,\sqrt{3}\,m\]

D)  80 m

Correct Answer: B

Solution :

[b] Let h be the height of kite above the ground.

In \[\Delta ABC,\]\[\sin 60{}^\circ =\frac{BC}{AB}\]

\[\Rightarrow \]   \[\frac{\sqrt{3}}{2}=\frac{h}{150}\]

\[\Rightarrow \]   \[h=\frac{\sqrt{3}\times 150}{2}\]

\[\Rightarrow \]   \[h=75\sqrt{3}\,m\]