Question

find the area of the sector formed by the angle 60° with a radius of 7.7. give your answer rounded to 2 decimal places.

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Here, \(\theta = 60^{\circ}\) and \(r = 7.7\). So \(A=\frac{60}{360}\times\pi\times(7.7)^{2}\).
First, simplify \(\frac{60}{360}=\frac{1}{6}\). Then \((7.7)^{2}=7.7\times7.7 = 59.29\).
So \(A=\frac{1}{6}\times\pi\times59.29\).

Step3: Calculate the value

\(A=\frac{59.29\pi}{6}\). Using \(\pi\approx3.14159\), we have \(A=\frac{59.29\times3.14159}{6}\).
\(59.29\times3.14159 = 59.29\times(3 + 0.14159)=59.29\times3+59.29\times0.14159=177.87+8.3973=186.2673\).
Then \(A=\frac{186.2673}{6}=31.04455\approx31.04\).

Answer:

\(31.04\)