Question

Find the length of each bolder arc to the nearest hundredth

Answer 1

Answer: For the bolded arc (angle of 107°) the lenght is 11.20 meters.

Step-by-step explanation:

Here we have two arcs.

one where the angle is 107°.

And for the other, we do not know the value of the angle, but we know that a circle has (between the start of quadrant 1 and the end of quadrant 4) an angle of 360°.

Then the missing angle is 360° - 107° = 253°.

Now, the length of an arc is equal to:

Arc = angle*pi*radius

where the angle is in radians, pi = 3.14.

In this case, the radius is = 6m.

To transform an angle from degrees to radians, we can do:

180° = 3.14

then for an angle A in degrees, we have: A => A*(3.14/180°) = (A/180°)*3.14

Then, the length of the shorter arc (the bolded one) is:

A1 = (107°/180°)*3.14*6m = 11.20m

For the other arc we do the same:

A2 = (257°/180°)*3.14*6m = 26.90 m