Question

As shown in the accompanying diagram, a dog is tied to a 16-foot leash,

which is attached to a corner where the house and fence meet. At this
corner, the angle between the house and the fence is 130°. When the dog
pulls the leash tight and walks from the house to the fence, what is the
distance that the dog walks, to the nearest tenth of a foot?
Backyard
Fence
(1) 11.6 feet
(2) 18.2 feet
(3) 32.0 feet
(4) 36.3 feet
House
(Not drawn to scale)

Answer 1

Find the circumference of the full circle:

Circumference = 2 x PI x radius.

The radius is given as the length of chain 16 feet.

Circumference = 2 x 3.14 x 16 = 100.48 feet.

The dog can walk 130 degrees.

Multiply the circumference by the fraction of a complete circle ( 360 degrees)

Distance = 100.48 x (130/360) = 36.28 feet

Round to 36.3 feet.

The answer is (4) 36.3 feet.