For #1.
Area triangle AOB = ([(3^1/2)/4]r^2)
Area sector AOB = (1/2)(r^2)(Angle in radians)
Area triangle AOB/ Area sector AOB = ([(3^1/2)/4]r^2)/(1/2)(r^2)(pi/3),
r^2 will cancel and 2 and simplifying
= 3[(3)^1/2]/2pi
Hi, I need some help with the following two problems:
1.) Find an exact value for the fraction of the sector represented by the triangle AOB in the sector AOB in the diagram.
The answer is supposedly 3√3/2π.
2). The area of the sector AOB and the triangle AOB are at a ratio of 3:2.
The angle AOB is in radians.
Show that 2θ-3sinθ=0.
I have managed to get:
3=½r²θ and 2=½r²sinθ
Therefore:
½r²θ-3=0 and ½r²sinθ-2=0
But I'm unsure where to go from there.
Any help would be appreciated. Thanks very much.
Hello evinyssen
Welcome to Math Help Forum!Thanks for showing us your working. You're almost there!
You're right in saying that the area of the sector is , and that the area of the triangle is . But you shouldn't then say that they are equal to and respectively. They are in the ratio ,which is a different thing.
We can always write a ratio as a fraction, so do just that:
Cancel the fraction on the LHS:
Grandad