Circle Trigonometry

[Kondwani Hauya]

The area of a sector of a circle is 15 cm^2 and the length of its arc is 3 cm. Calculate the radius of the sector and its angle.
Solution
r = 5 cm and angle = 3cm
Am I correct?

 

[MarkFL]

I don't agree with your results. Your angle will be in radians, not cm.

Can you show what you did?

 

[Kondwani Hauya]

Oh thanks for reminding me it's 3 radian.
I used two formulae:
formula for area of sector and formula for arc of a sector. By changing subject of for arc formula:
theta = 3cm/r which I substituted for theta in the formula for area of sector to find r as 5 cm. To find angle I used I substituted 5 cm for r in the formula of area of sector to get 3 radian

 

[MarkFL]

Okay, we have:

[MATH]s=r\theta\implies \theta=\frac{3}{r}[/MATH]
[MATH]A=\frac{1}{2}r^2\theta=\frac{3}{2}r\implies r=10\implies \theta=\frac{3}{10}[/MATH]

 

[Kondwani Hauya]

Why have you not used the area of sector (15cm^2) in the formula?

 

[MarkFL]

I did:

[MATH]A=\frac{3}{2}r\implies 15=\frac{3}{2}r\implies r=10[/MATH]

 

[Kondwani Hauya]

Now I get you. Thank you