Question

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at a 60° to the horizontal. Find the length of the string assuming that there is no slack in it.

Answer 1

Let $OX$ be the horizontal ground and $A$ be the position of the kite.
Also, let O be the position of the observer and $OA$ be the thread.
Now, draw $AB$⊥ $OX$.
We have:
∠$BOA\hspace{0.17em}=$${60}^o$, $OA=75$m and ∠$OBA\hspace{0.17em}={90}^o$
Height of the kite from the ground = $AB$ = 75 m
Length of the string, $OA\hspace{0.17em}=x$ m

In the right ∆$OBA$, we have:
$\frac{AB}{OA}=\sin {60}^o=\frac{\sqrt{3}}{2}$
⇒ $\frac{75}{x}=\frac{\sqrt{3}}{2}$
⇒ $x=\frac{75\times 2}{\sqrt{3}}=\frac{150}{1.732}=86.6$ m
Hence, the length of the string is $86.6$ m.