Question

A sector has an area of 942.5cm^2 and an arc length of 62.8cm what is the radius of the circle??

Answer 1

Arc length
\[s=r \theta\]
\[62.8=r \theta\]
\[r=\frac{62.8}{\theta}\]
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\[Area =\frac{1}{2}r^2 \theta\]
\[\frac{1}{2}(\frac{62.8}{\theta})^2 \theta=942.5\]
\[\theta=2.09~ radians\]
r=30

Answer 2

did you use a calculator of the computations?

Answer 3

For the formula, no
For the calculations for the answer, yes

Answer 4

how would I isolate the θ??

Answer 5

\[\frac{1}{2}(\frac{62.8}{\theta})^2 \theta=942.5\]
multiply 2 both sides
\[(\frac{62.8}{\theta})^2 \theta=1885\]
\[(\frac{62.8^2}{\theta^2}) \theta=1885\]
\[(\frac{62.8^2}{\theta^\cancel2}) \cancel\theta=1885\]
\[(\frac{62.8^2}{\theta}) =1885\]
\[(\frac{62.8^2}{1885}) =\theta\]

Answer 6

Thank you so very much.