Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

A garden has the shape of a circular sector such that its straight sides measure 50 feet in length and the central angle is 132°. if the garden needs to be surrounded by fencing, how many feet are needed to enclose the garden?

Sagot :

sqdancefan

Answer:

  215 ft

Step-by-step explanation:

The length of the surrounding fence is equal to the perimeter of the garden. That is the sum of the lengths of the straight sides and the curved arc. The arc length is given by the formula ...

  s = r·θ . . . . . where θ is the central angle in radians

__

arc length

There are π radians in 180°, so the arc will have a measure in radians of ...

  θ = 132° × (π/180°) = 11/15π ≈ 2.3038 . . . . radians

Then the length of the curved side of the garden is ...

  s = (50 ft)(2.3038 radian) ≈ 115.2 ft

__

perimeter

The fence length is the sum of the arc length and the two radii:

  perimeter = 115.2 ft + 2×50 ft = 215.2 ft

About 215 feet of fencing are needed to enclose the garden.

View image sqdancefan
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.