Question

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

Answer 1

`\boxed{\boxed{\theta=(\pi)/(3)}}`

Step-by-step explanation:

Hint -

`\text{Arc length}=r\theta\\\\\text{Area of the sector}=(1)/(2)r^2\theta`

Given here that,

`\theta=??\\\\r=3\\\\Area=(3)/(2)\pi`

So, putting all the values in the formula,

`\Rightarrow \text{Area of the sector}=(1)/(2)r^2\theta`

`\Rightarrow (3)/(2)\pi=(1)/(2)(3)^2\theta`

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

`\Rightarrow 3\pi=9\theta`

`\Rightarrow \theta=(3\pi)/(9)`

`\Rightarrow \theta=(\pi)/(3)`