Q&A for How to Use the Pythagorean Theorem

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What is the technical use of Pythagorean Theorem?

Donagan

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The Pythagorean Theorem allows you to find the length of one side of a right triangle when you know the lengths of the other two sides.

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Question

How can I find the slope dimension of a staircase?

Donagan

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Measure the horizontal and vertical distances from the top stair to the bottom stair, and use those two distances as "a" and "b" in the formula.

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How do I find the sides of a right triangle when I only have the length of the hypotenuse?

Community Answer

You can find the side with the help of an angle inside the triangle. Using sin of the angle gives you the opposite side divided by the hypotenuse or cos of the angle gives you the adjacent side divided with the hypotenuse.

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How do I prove that in a right angle triangle, the square on the hypotenuse is equal to the sum of the squared on the other two sides?

Donagan

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There are several ways to prove the Pythagorean Theorem (which is what you're asking). See one proof at mathisfun.com/geometry/pythagorean-theorem-proof.html.

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How do I find the base with just the hypotenuse?

Donagan

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You would have to know the other leg of the triangle. Knowing only the hypotenuse is not enough.

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How do I find the sides of a right triangle when I only have the length of the longest side?

Community Answer

You can't do it. If you know only the hypotenuse, the two legs could be any combination of lengths. For example, if the hypotenuse is 10 inches, the legs could be 8 and 6 inches, 4 and 9.166 inches, 2 and 9.8 inches, 5 and 8.66 inches, 7 and 7.14 inches, or an unlimited number of other combinations.

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Question

On a grid I draw the line segment for my points, got that part. But when I apply the distance formula and get, for example, 5 as my distance between points A and B, what tick marks am I counting on the grid that equal 5?

Donagan

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You can count "tick marks" on vertical and horizontal lines only, not on diagonal lines. The distance formula allows you to find the length of a diagonal line without having to measure or count it.

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