Question

hawa is flying a kite, holding her hands a distance of 3.75 feet above the ground and letting all the kite’s string out. she measures the angle of elevation from her hand to the kite to be 26°. if the string from the kite to her hand is 135 feet long, how many feet is the kite above the ground? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use sine - function to find height above hand

We know that in a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$ and the hypotenuse (length of the string) is $135$ feet. Let the height of the kite above the hand be $x$. So, $x = 135\times\sin(26^{\circ})$.
Since $\sin(26^{\circ})\approx0.4384$, then $x = 135\times0.4384 = 59.184$ feet.

Step2: Find height above ground

The height of the kite above the ground $h$ is the sum of the height of the hand above the ground ($3.75$ feet) and the height of the kite above the hand ($x$). So, $h=x + 3.75$.
Substitute $x = 59.184$ into the equation: $h=59.184+3.75=62.934\approx62.9$ feet.

Answer:

$62.9$ feet