SOLUTION: Carpenters and builders will sometimes measure 3 ft from a corner along one wall and 4 ft along the other, then check that it's 5 ft between the 2 points. If it is, the walls are "
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Question 199738: Carpenters and builders will sometimes measure 3 ft from a corner along one wall and 4 ft along the other, then check that it's 5 ft between the 2 points. If it is, the walls are "square", at right angles.
If the two short sides of a building are 3 and 4 how would you show carefully that you used the Pythagorean theorem to calculate the diagonal as 5?
You can put this solution on YOUR website! So solve your question, you must first find out the formula for Pythagorean Theorem.
The formula for that is a^2+b^2=c^2.
A and B being the legs.(3,4)
C being the hypotenuse. (in your case 5)
So plug in the numbers into the formula and then solve.
3^2+4^2=c^2
9+16=c^2
25=c^2
the square root of 25 = c^2
5=c
Therefore, you proved that the distance between those two walls are 5 feet
To check your answer just plug in the 5 into the formula.
3^2+4^2=25
9+16=25
25=25
You can put this solution on YOUR website! The Pythagorean Theorem is wriiten as follows:
Where:
a = one side of a right triangle
b = the other side of a right triangle
c = the hypoteneuse (diagonal) of a right trianagle
.
Note that this equation applies only to right triangles - which is a triangle which has one angle of 90 degrees. The hypoteneuse is the side of the triangle opposite this 90 degree angle.
.
So back to the problem... the goal is to make sure that the walls of the building are "square." That means that they form a 90 degree angle. So let's apply the pythagorean theorem to prove that if the 2 walls are length 3 and 4 respectively, the diagonal is 5.
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Pythagorean Theorem:
Substitute in your given values:
Simplify:
So you have proven that the diagonal is 5. Thus from the given information in the problem, you also know that the walls form a right angle.
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Good Luck,
tutor_paul@yahoo.com
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