Question

QuestionOn a circle with radius 12 m, what angle would subtend an arc with a length of 7 m?Give your answer in degrees, rounded to the nearest hundredth. In your answer, just enter the number - do not include"0 =" or the degrees symbol in your response.

Answer 1

The length of an arc is given as:

`l=(\theta)/(360)*2\pi r`

However, we don't seek "l" because it is already given. Our approach is to make the angle we seek the subject of the formula.

Given:

`\begin{gathered} l=(\theta)/(360)*2\pi r \\ \text{ We multiply 360 to both sides to get:} \\ 360l=\theta*2\pi r \\ \text{ We divide both sides by 2}\pi r\text{ to get} \\ (360l)/(2\pi r)=\theta \end{gathered}`

The angle is therefore:

`\theta=(360*7)/(2\pi*12)=33.42^o`

The angle subtended is 33.42 degrees