Question

A kite is flying with its string, which is of length 60 metres, taut.The kite is 20 metres vertically above the ground.a)Find the horizontal distance d between the ends of the string, giving the answerto 3 significant figures.b)Find the angle of elevation of the kite with the ground, giving the answer indegrees to 1 decimal place.

Answer 1

a) Due to you have a right triangle, in order to calculate the value of d, use the Pythagorean thorem:

$d=\sqrt[]{(60m)^2+(20m)^2}=\sqrt[]{4000m^2}\approx63.2m$

Hence, the distance d is approximately 63.2m

b) To find the angle of elevation, use the sine function of θ, as follow:

$\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse}=\frac{20m}{60m}=\frac{1}{3} \\ \theta=\sin ^{-1}(\frac{1}{3})\approx19.8 \end{gathered}$

Hence, the angle of elevation is approximately 19.8°