Question

If s denote the length of the arc of a circle of radius r subtended by a central angle, find the missing quantity.r=13.9 inches angle = 150 degrees

Answer 1

EXPLANATION

Given that the length of the arc of a circle of radius, the circunference is given by the following formula:

$\text{Circunference}=2\cdot\pi\cdot r$

We know that the total angle in a circle is 360 degrees, computing the circunference:

$\text{Circunference}=\text{ 2}\cdot\pi\cdot13.9$

Multiplying numbers:

$\text{Circunference =}\frac{139}{5}\pi=87.34\text{ inches}$

Since we have the subtended angle equal to 150 degrees, we can divide both numbers as shown as follows:

$150/360=\frac{5}{12}=0.42$

Hence, the total length is obtained by multiplying the Total Circunference by

the fraction as follows:

$Arc\text{ length = }0.42\cdot\text{ 87.34 = }36.68\text{ inches}$

In conclusion, the arc length is 36.68 inches