Shawna wanted to boat across the river, but did not know how wide it was. She walked along the shore for 90 feet and sighted across the water to the point she wanted to go. The angle that the sight line made with the shoreline was 65°. What was the distance across the river?

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Ответ:

Nathaliasmiles

01.04.2022

Mathematics

$x \approx 51.058\°$

or in radians

$x \approx 0.8911$

Step-by-step explanation:

We have the opposite side of angle x and hypotenuse of the right triangle.

$\text{sin}(\theta)= \frac{\text{opposite}}{\text{hypotenuse}}$

$\text{sin}(x)= \frac{14}{18}$

$\text{sin}(x)= \frac{7}{9}$

$x \approx 51.058\°$

Let's find the other side.

$18^2=14^2+b^2\\324=196+b^2\\b=\sqrt{128}$

$b=8\sqrt{2}$

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