Question

A gazebo is located in the center of a large circular lawn with a diameter of 200 feet. Straight paths extend from the gazebo to a sidewalk around the lawn. If two of the paths form an 85° angle, how far would you have to travel around the sidewalk to get from one path to the other? Show all necessary work and calculations to receive full credit.

Answer 1

Answer:

  about 148 feet

Step-by-step explanation:

You want to know the distance between two points on a 200 ft circle that are separated by a central angle of 85°.

Circumference

The full 360° arc of the circle is its circumference, found using the formula ...

  C = πd

  C = π(200 ft) ≈ 628.3185 ft

Fraction

The portion of that distance that subtends an 85° arc is proportional to the measure of the arc:

  distance between paths = (628.3185 ft) × (85°/360°) ≈ 148.4 ft

You would have to travel about 148 ft to get from one path to the other.

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Additional comment

We have assumed you want to go the short way. The long way will be the difference between the full circumference and this short distance:

  628.32 ft -148.35 ft = 479.96 ft

It is about 480 ft if you go the long way around.