A kite is flying with a thread 80 m long. If the thread is assumed stretched straight and makes an angle of 60° with the horizontal, find the height of the kite above the ground.

Let AC be the length of string = 80 m and height of kite above ground be AB (h).

Angle of elevation = 60°

In triangle ABC,

$\Rightarrow \sin \theta = \dfrac{\text{perpendicular}}{\text{hypotenuse}} \\[1em] \Rightarrow \sin 60° = \dfrac{h}{80} \\[1em] \Rightarrow \dfrac{\sqrt3}{2} = \dfrac{h}{80} \\[1em] \Rightarrow h = 80 \times \dfrac{\sqrt3}{2} \\[1em] \Rightarrow h = 40 \times 1.732 \\[1em] \Rightarrow h = 69.28 \text{ m}$

Hence, height of the kite above the ground is 69.28 m.