A circle has a circumference of 12. It has an arc of length 8/5. what is the central angle of the arc, in degrees?

Mathematics

2 answers:

earnstyle [38]2 years ago

6 0

360⁰......12

x.............8/5=1.6

Thus:

x=1.6×360/12=1.6×30=48⁰

Answer: x=48⁰

77julia77 [94]2 years ago

5 0

Answer: The central angle of the arc is 48 degrees.

Step-by-step explanation: The question has provided the first clue, which is the circumference of the circle, given as 12 units. Also the length of an arc along the same circumference has been given as 8/5 units. The circumference of a circle is calculated as

Circumference = 2Pi x radius

Also the length of an arc is calculated as

Length of an arc = (X/360) x 2Pi x radius (where ‘X’ is the angle subtended by the arc).

Having known the answer to 2Pi x radius which is 12, and the length of the arc which is 8/5, we can now express the length of an arc as

Length of an arc = (X/360) x 2Pi x radius

8/5 = (X/360) x 12

By cross multiplication we now have

(8 x 360)/ (5 x 12) = X

2880/60 = X

48 = X

Therefore the central angle of the arc is 48 degrees.

You might be interested in

The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. He wants to first determin

bulgar [2K]

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, $Z_{Critical}=1.645$ .

We also know that E=5% or E=0.05

Also, since, $\hat{p}$ is not given, we will assume that $\hat{p}$ =0.5. This is because, the formula that we use will have $\hat{p}(1-\hat{p})$ in the expression and that will be maximum only when $\hat{p}$ =0.5. (For any other value of $\hat{p}$ , we will get a value less than 0.25. For example if, $\hat{p}$ is 0.4, then $1-\hat{p}=0.6$ and thus, $\hat{p}(1-\hat{p})=0.24$ .).