How To Solve A Pythagorean Theorem Problem

How To Solve A Pythagorean Theorem Problem-7
If you're behind a web filter, please make sure that the domains *.and *.are unblocked.The Pythagorean theorem is a way of relating the leg lengths of a right triangle to the length of the hypotenuse, which is the side opposite the right angle.

If you're behind a web filter, please make sure that the domains *.and *.are unblocked.The Pythagorean theorem is a way of relating the leg lengths of a right triangle to the length of the hypotenuse, which is the side opposite the right angle.

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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.

Write an expression that shows the value of \(y\) in terms of \(x\).

Since no figure was given, your first step should be to draw one.

If the distance between the two building is 12 m, find the distance between their tops.

Solution: The vertical buildings AB and CD are 34 m and 29 m respectively.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.Even though it is written in these terms, it can be used to find any of the side as long as you know the lengths of the other two sides.In this lesson, we will look at several different types of examples of applying this theorem.Due south and due west form a right angle, and the shortest distance between any two points is a straight line.Therefore, we can apply the Pythagorean theorem and write: \(3.1^2 2.8^2 = x^2\) Here, you will need to use a calculator to simplify the left-hand side: \(17.45 = x^2\) Now use your calculator to take the square root. \(\beginx &= \sqrt \ &\approx 4.18 \text\end\) As you can see, it will be up to you to determine that a right angle is part of the situation given in the word problem.The order of the legs isn’t important, but remember that the hypotenuse is opposite the right angle.Now you can apply the Pythagorean theorem to write: \(x^2 y^2 = (2x)^2\) Squaring the right-hand side: \(x^2 y^2 = 4x^2\) When the problem says “the value of \(y\)”, it means you must solve for \(y\).Therefore, we will write: \(y^2 = 4x^2 – x^2\) Combining like terms: \(y^2 = 3x^2\) Now, use the square root to write: \(y = \sqrt\) Finally, this simplifies to give us the expression we are looking for: \(y = \bbox[border: 1px solid black; padding: 2px]\) The Pythagorean theorem allows you to find the length of any of the three sides of a right triangle.It is one of those things that you should memorize, as it comes up in all areas of math, and therefore in many different math courses you will probably take.

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