Question

find the area of the sector of a circle with radius 8 feet formed by a central angle of 85°: square feet round your answer to two decimal places. question help: worked example 1 message instructor

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the given values into the formula

Given \(r = 8\) feet and \(\theta=85^{\circ}\).

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Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A=\frac{136\times3.14159}{9}\approx\frac{427.25624}{9}\approx47.47\)

Answer:

\(47.47\)