Grazing With the Goat

by

Priscilla Alexander

This write-up is for students have taken geometry and trigonometry who are interested in the following scenario.

Farmer Jones had a goat on a tether. He tied the end of the tether not attached to the goat to a stake in a field. Over what area could the goat graze?

There are two structrues in the field:

-- a shed is 20 ft long and 20 ft wide (square)

-- a silo that is 20 ft in diameter

The center of the shed and the center of the silo are on a line and the distance apart is 92 ft. The tether for the goat is 76.7 feet long. The stake to which the tether is tied is somewhere along the line of centers between the shed and the silo.

Explore the area of which the goat can graze as the stake moves long the line segment from the midpoint of the side of the shed to the edge of the silo.

Investigation

Case 1: What is the area the goat can graze if the stake is at the midpoint of the barn?

Case 2: What is the area the goat can graze when the stake is at the outter edge of the silo.

See GSP

In conclusion, the goat can graze more of the field if the tether is staked at the silo. A possible reasoning for this is that the silo takes up less of the field therefore the goat can graze more of the field at that end. In other words, the goat can gaze the area more of the area in the back of the silo in addition to the area in front of the silo. The area in the front of the silo consist of the area of the field the goat can graze, according to the length of the tether.

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