Help on Radian Measure of Angles Question. Find the area covered by the wiper.?

A car's rear windshield wiper rotates 135 degrees.

The wiper mechanism has a total length of 23 inches

and wipes the windshield over a distance of 14 inches.

Find the area covered by the wiper.

Convert 135° to radians:

θ

= 135 * (π/180) radians

= 3π/4 radians

Arc radius = 14 inches

Area of a sector of a circle = (1/2) * r^2 * θ

A_23 = (1/2) * (23^2) * (3pi/4) = 15625pi/72 ≈ 217pi in^2

A_11 = (1/2)(11^2)(25pi/36) = 3025pi/72 ≈ 42pi in^2

A = 217pi - 42pi = 175pi in^2

Convert 135° to radians:

θ

= 135 * (π/180) radians

= 3π/4 radians

Area of a sector of a circle = (1/2) * r^2 * θ

A_23 = (1/2) * (23^2) * (3π/4) = 1587 π/8

A_9 = (1/2) * (9^2) * (3π/4) = 243 π/8

Area covered by the wiper

= 1344 π/8

≈ 527.7875658... in^2