Question

1. choose the correct answer.

cynthia is flying a kite in her back pasture. she has let out 50 meters of kite string and the string makes an angle of elevation with the ground of 42°. how high is the kite flying, to the nearest tenth of a meter?
50 m
42°
x
16.5 m
33.5 m
47.2 m
24.6 m

Explanation:

Step1: Identify trigonometric ratio

We use sine, since $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=42^\circ$, hypotenuse $=50$ m, opposite side $=x$ (height).

Step2: Substitute values into formula

$$\sin(42^\circ)=\frac{x}{50}$$

Step3: Solve for $x$

Rearrange to isolate $x$: $x=50\times\sin(42^\circ)$
Calculate $\sin(42^\circ)\approx0.6691$, so $x\approx50\times0.6691=33.455$

Step4: Round to nearest tenth

$33.455\approx33.5$

Answer:

B. 33.5 m