A bug lands on a windshield wiper blade before it is flung off. The wiper blade and arm assembly have a length of 30 inches. If the blade passed through an angle of 68 degrees before the bug is thrown off, how far has the bug traveled?

35.6047 inches

Step-by-step explanation:

The wiper blade moves in a circular way, where the radius is 30 inches.

To find how far the bug travelled, we just need to use a rule of three, where the length of the circunference relates to a angle of 360 degrees:

360 degrees -> 2 * pi * radius

68 degrees -> distance

distance * 360 = 2 * pi * radius * 68

distance = 2 * pi * 30 * 68 / 360 = 35.6047 inches

35.58 inches

Step-by-step explanation:

The distance that the bug travels is equal to the arc of the circle where the radius is 30 inches and the angle is 68°

The arc can be written as:

A = angle*r

where the angle is in radians, we know that:

180° = 3.14

then:

68° = (68°/180°)*3.14 = 1.19 radians.

Then the arc is:

A = 1.19*30in = 35.58 inches