Question

What is the measure of 0(theta) in radians if r=3 & the area is 3pi/2?

Answer 1

Answer:

$\boxed{\boxed{\theta=\dfrac{\pi}{3}}}$

Explanation:

Hint -

$\text{Arc length}=r\theta\\\\\text{Area of the sector}=\dfrac{1}{2}r^2\theta$

Given here that,

$\theta=??\\\\r=3\\\\Area=\dfrac{3}{2}\pi$

So, putting all the values in the formula,

$\Rightarrow \text{Area of the sector}=\dfrac{1}{2}r^2\theta$

$\Rightarrow \dfrac{3}{2}\pi=\dfrac{1}{2}(3)^2\theta$

$\Rightarrow 3\pi=(3)^2\theta$

$\Rightarrow 3\pi=9\theta$

$\Rightarrow \theta=\dfrac{3\pi}{9}$

$\Rightarrow \theta=\dfrac{\pi}{3}$