SOLUTION: A farmer is building a pen inside a barn. The pen will be the shape of a right triangle. The farmer has 14 feet of barn wall to use for one side of the pen and wants another side

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Question 954437: A farmer is building a pen inside a barn. The pen will be the shape of a right triangle. The farmer has 14 feet of barn wall to use for one side of the pen and wants another side of the pen to be 15 feet long.
a) How many different lengths for the third side are possible? Explain.
b) To the nearest tenth of a foot, find all possible lengths for the third side of the triangle. Show your work.
c) The farmer wants the area of the pen to be as large as possible. What length should he choose for the third side? Justify your answer.
d) Find the measure of the acute angles for the triangle you described in part (c). Round to the nearest degree.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A). There are two possible lengths for the third side: one as the hypotenuse and one with the 15 foot side as the hypotenuse.
.
B).
a%5E2%2Bb%5E2=c%5E2
14%5E2ft%5E2%2B15%5E2ft%5E2=c%5E2
196ft%5E2%2B225ft%5E2=c%5E2
421ft%5E2=c%5E2
20.5ft=c ANSWER: One possibility is 20.5 feet.
.
b%5E2=c%5E2-a%5E2
b%5E2=15%5E2ft%5E2-14%5E2ft%5E2
b%5E2=225ft%5E2-196ft%5E2
b%5E2=29ft%5E2
b=5.4ft ANSWER: The other possibility is 5.4 feet.
.
C).
Area for choice a=%281%2F2%29bh=%281%2F2%29%2814ft%29%2815ft%29=105ft%5E2
Area for choice b=%281%2F2%29bh=%281%2F2%29%285.4ft%29%2814ft%29=75.6ft%5E2
ANSWER: The farmer should choose 20.5 feet for the third side.
.
D)
arctan(14/15)=43 degrees
90 degrees-43 degrees=47 degrees
ANSWER: With the third side 20.5 feet, the angles are 43 and 47 degrees.
arctan(5.4/14)=21 degrees
90 degrees-21 degrees=69 degrees
ANSWER: With the third side 5.4 feet, the angles are 21 and 69 degrees.