# How To Solve A Pythagorean Theorem Problem

Remember though, that you could use any variables to represent these lengths.

Remember though, that you could use any variables to represent these lengths.

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This is common unless you are working on an applied problem.

There are many different kinds of real-life problems that can be solved using the Pythagorean theorem.

You can still use the Pythagorean theorem in these types of problems, but you will need to be careful about the order you use the values in the formula. The side opposite the right angle has a length of 12.

Therefore, we will write: $$8^2 y^2 = 12^2$$ This is the same as: $$64 y^2 = 144$$ Subtracting 64 from both sides: $$y^2 = 80$$ Therefore: $$\beginy &= \sqrt \\ &= \sqrt \\ &= \bbox[border: 1px solid black; padding: 2px]\end$$ In this last example, we left the answer in exact form instead of finding a decimal approximation.

After one hour, the hiker walking south has covered 2.8 miles and the hiker walking west has covered 3.1 miles.

At that moment, what is the shortest distance between the two hikers? Label any unknown value with a variable name, like x.

This is something that you will not need to do in every course, but it does come up.

A right triangle has a hypotenuse of length $$2x$$, a leg of length $$x$$, and a leg of length y.

But, the length of any side of a triangle can never be negative and therefore we only consider the positive square root.

In other situations, you will be trying to find the length of one of the legs of a right triangle.

## Comments How To Solve A Pythagorean Theorem Problem

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It is called "Pythagoras' Theorem" and can be written in one short equation a 2 + b 2 = c 2. Note c is the longest side of the triangle; a and b are the other two sides ; Definition. The longest side of the triangle is called the "hypotenuse", so the formal definition is…

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Find the length of the hypotenuse or a leg of a right triangle using the Pythagorean theorem. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.and *.are unblocked.…

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