SOLUTION: Suppose at the kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field. How many yards

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Question 77186: Suppose at the kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field. How many yards would he run? (A football field is 100 yards long and 60 feet wide.)
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Your information is flawed. In all three environments (professional, college, and high school)
the dimensions of a football field are 100 yds from goal line to goal line and 160 ft (not 60 ft)
from sideline to sideline (160 ft = 53 and 1/3 yds or approximately 53.3333 yds).
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Since it may just have been a keyboarding error on your part, I'm going to use 53.3333 yds
as the distance between sidelines.
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The given problem can be solved using the Pythagorean theorem. From where the player
catches the football at the goal line corner, the player runs diagonally down the field to
the opposite goal line corner. This diagonal is the hypotenuse of a right triangle.
The two legs of the right triangle would have been traveled if instead of running the
diagonal the player had run along the sideline to the other goal line and then turned 90
degrees and run along the goal line to the opposite corner.
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In following this sideline path the player would have run the 100 yd length of the field
and then turning 90 degrees and running along the goal line to the opposite corner would
have been the second leg and would have been the 53.3333 yd width of the field.
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The Pythagorean theorem says that the sum of the squares of the two legs of a right
triangle is equal to the square of the hypotenuse. We are trying to find the hypotenuse
(h) which is the diagonal across the field, and we know that the two legs are 100 yds and
53.333 yds.
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Substituting our known values into the Pythagorean relationship we get:
.

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Squaring the two terms on the left side results in:
.

.
Adding the numbers on the right side gives you:
.

.
and then you solve for the hypotenuse (h) by taking the square root of both sides to
find that:
.

.
So by cutting in a straight line across the field, the player runs 113.3333 yards,
or approximately 113 and 1/3 yards.
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Hope that this problem is correct for you. However, if you really meant that the field
was to be 60 ft wide (or 20 yds), then you need to go back and substitute 20 wherever
you see 53.3333 yds above and you should then find that the player runs 101.9804
yds in crossing the field diagonally between goal lines.