Question

1. a boy is flying a kite with a string which forms a 41° angle with the ground and is extended to a length of 180 m from the ground. calculate the height of the kite above the ground.

Explanation:

Step1: Identify the trigonometric relationship

We can use the sine - function in a right - triangle. Let the height of the kite above the ground be $h$, the length of the string be the hypotenuse $c = 180$ m and the angle between the string and the ground $\theta=41^{\circ}$. The formula for sine is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin\theta=\sin41^{\circ}$ and the opposite side to the angle $\theta$ is the height $h$ of the kite, and the hypotenuse $c = 180$ m. So, $\sin41^{\circ}=\frac{h}{180}$.

Step2: Solve for $h$

We can re - arrange the formula $\sin41^{\circ}=\frac{h}{180}$ to get $h = 180\times\sin41^{\circ}$. We know that $\sin41^{\circ}\approx0.6561$. Then $h = 180\times0.6561$.
$h=118.098\approx118.1$ m.

Answer:

$118.1$ m