Step by step
The question
Question: find the arc length s of a circle with radius 5 and angle 2 radians.
The arc is the curved part of the edge.
We know the radius: r = 5.
r = 5
And the angle: θ = 2 radians.
θ = 2
1 Write the rule
The rule for the arc length: s = rθ.
θ must be in radians.
s = rθ
Why?
A full turn is 2π.
Then s is 2π times r: the whole edge of the circle.
A smaller angle gives a part of it.
θ = 2π: s = 2πr, the whole edge
Careful!
The rule only works with the angle in radians.
Ours already is.
Careful: θ in radians, not degrees
2 Put the numbers in
Now put the numbers in: r = 5 and θ = 2.
s = 5 × 2
3 Work it out
5 times 2 is 10.
So s = 10.
s = 10
4 Check
Let's check: the arc over the radius gives the angle back.
105 = 2
We get 2: the angle.
So it is right!
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: work it out.
Last: check.
Answer
s = 10