Question

solve. round answers to the nearest tenth when necessary (one decimal place).
isabella has attached her kite to a stake in the ground. she lets out 89 feet of string.
the kites angle of elevation with the ground is $40^\circ$. if the string is stretched tight,
how high is the kite flying?
_______ feet

Explanation:

Step1: Define trigonometric relationship

We use the sine function, where $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 40^\circ$, hypotenuse = 89 feet, and the opposite side is the height $h$ we need to find.

Step2: Rearrange to solve for height

Rearrange the formula to isolate $h$: $h = 89 \times \sin(40^\circ)$

Step3: Calculate the value

First, find $\sin(40^\circ) \approx 0.6428$, then compute:
$h \approx 89 \times 0.6428$
$h \approx 57.2092$

Step4: Round to nearest tenth

Round 57.2092 to one decimal place: $h \approx 57.2$

Answer:

57.2 feet