Question

question
a sector of a circle has an area of 10 square feet. find the central angle which forms the sector if the radius is 2 feet.
the central angle of the sector is $square$ radians.
(type an integer or a simplified fraction.)
question | 1/1 pt
6.2.4
question | 1/1 pt
6.2.5
question | 0/1 pt
6.2.6
question | 0/1 pt
6.2.7

Explanation:

Step1: Recall sector area formula

The formula for the area \(A\) of a sector with radius \(r\) and central angle \(\theta\) (in radians) is \(A = \frac{1}{2}r^2\theta\).

Step2: Plug in known values

Substitute \(A = 10\) and \(r = 2\) into the formula:
\(10 = \frac{1}{2}(2)^2\theta\)

Step3: Simplify and solve for \(\theta\)

First calculate \((2)^2 = 4\), then \(\frac{1}{2} \times 4 = 2\):
\(10 = 2\theta\)
Divide both sides by 2:
\(\theta = \frac{10}{2} = 5\)

Answer:

5