Question

Circle O shown below has a radius of 27 inches. Find, to the nearest tenth of adegree, the measure of the angle, 2, that forms an are whose length is 14 inches.

Answer 1

The measure of the central angle subtended by the arc is 29.7 degrees

Finding the measure of the central angle of the arc

From the question, we have the following parameters that can be used in our computation:

The arc

Where, we have

Radius = 27 inches

Arc length = 14 inches

Using the above as a guide, we have the following:

Arc Length = central angle/180 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

14 = central angle/180 * 3.14 * 27

So, we have

Central angle = (14 * 180)/(3.14 * 27)

Evaluate

Central angle = 29.7

Hence, the measure of the central angle of the arc is 29.7 degrees

Answer 2

To calculate the value of x the length of arc formula will be used

The formua for length of arc is

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

From the given circle

L= 14

r=27

Substitute the values into the formula

`14=(x)/(360)*2\pi*27`

Solve for x

`\begin{gathered} 14*360=54\pi x \\ 5040=54\pi x \\ x=(5040)/(54\pi) \end{gathered}`

Hence the value of x is

`x=29.7^(\circ)`

Therefore the required angle is 29.7⁰