In a baseball field, home plate and the three bases are supposed to be the corners of a square. Do the directions below result in home plate and the three bases being the corners of a square?

Question

The Major League Baseball website provides instructions for laying out a basball field: “when the location of home plate is determined, use a steel tape (tape measure) to measure 127 feet, 3 3/8 inches in the desired direction to establish second base. From home plate measure 90 feet towards first base. From second base measure 90 feet towards first base. The intersection of these lines locates first base.” Third base is found in a similar manner, but to the left of home plate instead of to the right.

2. Give a description of how you would use the Pythagorean Theorem to determnine whether creating home plate and the 3 bases as directed above creates a square. If it doesn't make a square, how close is it to being a square (your answer should be a number, not words like "very close")?

3. Give a description of how you would use the Law of Cosines to determine whether creating home plate and the 3 bases as directed above creates a right angle at first base. If it doesn't make a right angle at first base, how close is it to being a right angle (Again, your answer should be a number, not words like "really close")?

PLEASE HELP ASAP!!

Answer 1

d^2=2(90)^2=2(8100)=16200

d=sqr16200=10sqr162= about 127 ft 8 in >127 ft 3 3/8 in

not exactly a square

(127 27/96)^2 = 2(90^2)-2(90^2)cosD

16200,5166= 16200-16200cosD

cosD=about-.5166/16200

D=about 90.0018 degrees

D>pi/2

not exactly a right angle

about 0.0018 degree too large

but if you rounded off to the nearest hundredth of a degee it is a right angle

and a square