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 =}(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=(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