Question

An arc of length 30 meters is formed by a central angle A on a circle of radius 15. The measure of A in degrees (to two decimal places) is?

A) 0.50
B) 28.65
C) 114.59
D) 0.01

How do I go about solving this?

Answer 1

Ratio

\(\dfrac{A}{30} = \dfrac{360}{2\pi\cdot 15}\)

Arc Length is to the circumference as the Central Angle is to the whole 360º.

Arc Length (30) is to the circumference (\(2\pi\cdot 15\)) as the Central Angle (A) is to the whole 360º.

Answer 2

@tkhunny Is there another step?

Answer 3

Nope. Unless you count a little arithmetic.

Answer 4

Oh, so...what exactly should be done with that formula there?

Answer 5

Do you yet know the value of "A"? If not, you should find it.

Answer 6

@tkhunny 114?

Answer 7

You tell me. How did you get that?

Answer 8

@tkhunny multiplaied 2 by 15, got 30. Multiplied 30 by pi and got 94.2. That left me with \[A/30=360/94.2\]. REduced the right side to 3.8217, multiply by 30, simplified the left side, and multiplied the result by 30.

Answer 9

It appears you are left only with severe rounding problems.

You may consider this: \(\dfrac{A}{30} = \dfrac{360}{30\pi}\)

Multiply by 30: \(A = \dfrac{360}{\pi}\)

This seems to have made life quite a bit easier. \(A = 360/\pi\)

Answer 10

Based on that A=114