Question

A dog tied by a rope to a pole moves through an angle of 35° along a circular arc. how far does the dog move the rope is 30 feet in length

Answer 1

The dog moves approximately 5.30 feet when it is tied to a 30-foot rope and moves through an angle of 35° along a circular arc.

Step-by-step explanation:

To determine how far the dog moves when it is tied to a pole with a 30-foot rope and moves through an angle of 35° along a circular arc, we can use the formula for the length of a circular arc:

Length of Arc = (Angle in Radians) x (Radius)

Since the angle is given in degrees, we need to convert it to radians. 1 radian is equal to 180/π degrees. Therefore, the angle in radians is:

Angle in Radians = (35°) x (π/180)

Next, we can substitute the known values into the formula and calculate the length of the arc:

Length of Arc = (Angle in Radians) x (Radius) = (35° x (π/180)) x (30 feet) = approximately 5.30 feet

Therefore, the dog moves approximately 5.30 feet when it is tied to a 30-foot rope and moves through an angle of 35° along a circular arc.