a horse is tied to a pole by a rope if the horse moves along a circular path keeping the rope tight and describe 176 m when it has traced out 72degree at the pole find the length of the rope
The 176 m line is a circular arc.
72 degrees is 1.2566 radians
176 m = 1.2566* R
Solve for R (rope length)
R = 140.06 meters
To find the length of the rope, we can use the concept of the circumference of a circle.
When the horse moves along a circular path, the distance it travels is equal to the length of the rope. In this case, the distance traveled is 176 m when it has traced out an angle of 72 degrees at the pole.
To find the length of the rope, we can set up a proportion based on the relationship between the distance traveled and the angle traced out:
Distance traveled / Circumference of the circle = Angle traced out / 360 degrees
Plugging in the given values, we have:
176 m / Circumference of the circle = 72 degrees / 360 degrees
Simplifying the equation:
176 m / Circumference of the circle = 1/5
To find the length of the rope, we need to find the circumference of the circle. Rearranging the equation, we get:
Circumference of the circle = 176 m / (1/5)
Dividing 176 m by 1/5:
Circumference of the circle = 176 m * 5
Circumference of the circle = 880 m
Therefore, the length of the rope is 880 meters.