C2 Area of a sector Watch

Eddy!
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#1
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I know how to work out the area of a sector when given the angle and radius, however I'm not too sure how to work back from being given the area to finding the angle.

The question is...
A sector has an area of 20cm(squared) and radius 8cm. What angle, in degrees, does it subtend at the centre?

Help would be appreciated.
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Zishi
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A = \frac{1}{2} r^2 \theta

Use this to find angle in radians, and to convert the angle into degrees, use:

360o : 2\pi
xo : (Your angle in radians)

Use this ratio method to convert it.

I hope it helps.
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Kidneyjean
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You would do 20cm^2 = 0.5(unknown angle)8^2

Then solve to find the unknown angle (it would be in radians).
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tiny hobbit
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(Original post by Eddy!)
I know how to work out the area of a sector when given the angle and radius, however I'm not too sure how to work back from being given the area to finding the angle.

The question is...
A sector has an area of 20cm(squared) and radius 8cm. What angle, in degrees, does it subtend at the centre?

Help would be appreciated.
Substitute the numbers into A=0.5r^2 theta and you'll have an equation for theta (theta will be in radians)
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gdunne42
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Area = (Angle/360) x pi x r^2

rearrange the formula to make Angle the subject

Area/(pi x r^2)= Angle/360

(360 x Area)/(pi x r^2) = Angle (in degrees as requested)
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