Question

Find the length of AB.6 in A30°BAB = [ ? ]in=Round your answer to the nearest hundredth.

Answer 1

Hello there. To solve this question, we'll have to remember some properties about arcs and angles in a circle.

Given the arc AB in the following circle:

We have to determine its length.

For this, remember that given an arc, the angle and the radius of the circle, we can find its length in the following way:

Where C is the length of the circumference, given by the formula:

`C=2\pi R`

Such that we get:

Of course, the angle alpha is in radians. To convert an angle in degrees to radians, we apply the formula:

Therefore, we apply this formula by plugging Angle = 30º:

`\alpha=30^(\circ)\cdot(\pi)/(180^(\circ))=(\pi)/(6)`

Now, we plug this angle in the formula, also plugging R = 6 in, such that

This is the length of this arc.