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# A water sprinkler sprays water on a lawn over a distance of 25 feet and rotates through an angle of 130°. Find the area of the lawn watered by the sprinkler.

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Answered 2 years ago
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We need to find the area of the lawn watered by the sprinkler.

We have a distance of 25 feet and angle of $130 \text{\textdegree}$.

First, let's convert a given angle from degrees to radians using the formula:

$\text{ radians }=\text{ degrees } \cdot \frac{\pi}{180 \text{\textdegree}}$

Therefore,

$130 \text{\textdegree} \cdot \frac{\pi}{180 \text{\textdegree}}=\frac{13\pi}{18}\approx 2.27$

Hence, the formula for the area of the lawn formed by the water is:

$A=\frac{1}{2}r^2\cdot 2.27$

and as the radius is $r=25$ feet, we obtain that the area is :

$A=\frac{1}{2}\cdot 25^2 \cdot 2.27\approx 709.4 \text{ feet}^2$

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