Answer:
about 0.4784 radians, or 27.4°
Step-by-step explanation:
You want the central angle of a sector that has an area of 350 m² and an arc length of 18.3 m.
Formulas
The formula for arc length is ...
s = rθ
The formula for area of a sector is ...
A = 1/2·r²θ
These tell us we can find the central angle θ from ...
[tex]\theta=\dfrac{s^2}{2A}=\dfrac{(r\theta)^2}{2(\dfrac{1}{2}r^2\theta)}=\dfrac{r^2\theta^2}{r^2\theta}[/tex]
Application
Using the given values, we find the angle (in radians) to be ...
[tex]\theta=\dfrac{18.3^2}{2(350)}\approx\boxed{0.4784\text{ radians}\approx27.4^\circ}[/tex]
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Additional comment
We can find the radius of the circle from s/θ = r ≈ 18.3/0.4784 ≈ 38.25 m.
