Question

Calculate the arc length of S & area A of the following sector. Round to the nearest whole number

Answer 1

The formulas for the arc length s and the area A of a circular sector are:

$\begin{gathered} s=\theta\cdot r \\ A=\frac{\theta\cdot r^2}{2} \end{gathered}$

Where θ is the angle (in radians) and r is the radius. From the problem, we know that:

$\begin{gathered} \theta=0.7\text{ rad} \\ r=170\text{ ft} \end{gathered}$

Then, using the formulas above:

$\begin{gathered} s=0.7\cdot170=119\text{ ft} \\ A=\frac{0.7\cdot170^2}{2}=10115\text{ ft}^2 \end{gathered}$