Pythagorean Therom?

Question

A football field is to measure 50.3 meters by 100.6 meters. Workers laying the chalk lines must ensure that the corners of the field form right angles. Explain how they can use the Pythagorean therom to help them.

Answer 1

They can calculate the diagonal (hypotenuse) and use the equality of the two diagonals as a cross check about the corners being of right angles. If the corners are not at right angles, one diagonal will be more than the other.

Answer 2

This is the easiest way to determine if a corner is 90 degrees. It is a very common trick that woodworkers and carpenters use and is based on the Pythagorean Theorm. Here is how it is done. It is called the 3, 4, 5 rule. What it means is if you measure a distance down the endline from one corner say 30 feet and mark that point. Now measure down the sideline from that corner say 40 feet and mark that point. Next measure from the point you marked on the endline to the point you marked on the sideline. If the corner is square the distance between the points will be 50 feet. How is the 3,4,5 rule based on the Pythagorean Theorm? Here is the answer:

a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
As you can see it does not have to be exactly 3,4,5. It can be multiples of 3,4,5 too.

You could also substitute the numbers you gave to give:

50.3^2 + 100.6^2 = c^2
2530.09 + 10120.36 = c^2
12650.45 = c^2
c = 112.47 meters
The corner is square if you measure the diagonal across the field and it is 112.47 meters. I really hope this helps you out.

Answer 3

Split the pitch up into 2 triangles, with a line from one corner to the other. Now use pythag therom on the sides of one of the triangles.

a^2 + b^2 = h^2
100.6^2 + 50.3^ = h^2
10120.36 + 2530.09 = h^2
h^2 = 12650.45
root 12650.45 = approx 112.5

If both triangles have the same hypotenuse length then they are at right angles if laid correctly.

Answer 4

Ensure that the diagonal is equal to the square root of 50.3 ^2 + 100.6^2.

50.3^2 + 100.6^2 = x^2
X^2 = 2530.09 + 10120.36
x^2 = 12650.45
x = 112.47 meters
Make the Diagonal 112.47 meters

Answer 5

You use the therom .. a^2+b^2=c^2.
So (50.3)^2+(100.6)^2=c^2 .. and c is the diagonal. So solve .. 10373.45=c^2 .. c= 101.85
If both diagonals measure that, then you have right angles.

Answer 6

Assuming that the workers cannot measure a right angle directly...
A 50.3m straight line is drawn. Worker A holds a 100.6m thread from one point of the line so that the thread is tensed. Another worker B brings up a 112.4 m thread walks straight towards the first. For the other side, workers interchange their positions and the end point of the two lines are then joined together.

Answer 7

he measures the diagonal
if its equal to
50.3^2+100.6^2
then its true
pyth: a^2=b^2+c^2 where a is the side facing the right angle
the inverse of this equations gives you ur result!!

Answer 8

There are probably more proofs of the Pythagorean theorem than of any other theorem.