How is the Pythagorean theorem used?

To find side lengths of a right triangle.

How do you find a missing leg in a right triangle?

Use the Pythagorean theorem and isolate the unknown side.

Hypotenuse, legs, and right angle.

Essential for solving geometric problems involving right triangles.

The Pythagorean theorem is a mathematical principle used to determine the lengths of the sides of a right triangle, where the square of the hypotenuse equals the sum of the squares of the other two sides.
By applying the Pythagorean theorem formula a^2 + b^2 = c^2, one can calculate the missing side lengths of a right triangle, whether it is the hypotenuse or one of the legs, by isolating the unknown variable and solving for it.

How is the Pythagorean theorem used?
To find side lengths of a right triangle.
What is the formula for finding the hypotenuse?
a^2 + b^2 = c^2
How do you find a missing leg in a right triangle?
Use the Pythagorean theorem and isolate the unknown side.
What are the components of a right triangle?
Hypotenuse, legs, and right angle.
Why is the Pythagorean theorem important?
Essential for solving geometric problems involving right triangles.

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The Pythagorean theorem is used to find unknown side lengths of a right triangle, with C as the hypotenuse and A and B as the legs.
To find the length of the hypotenuse, use the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
In an example with side lengths of 8 meters and 6 meters for the legs, applying the formula gives a hypotenuse length of 10 meters.
Another example involves side lengths of 10 feet and 7 feet for the legs, resulting in an approximate hypotenuse length of 12.21 feet.
To find the length of a missing leg, use the same formula and isolate the unknown side by solving for it.
In an example with a leg of 5 yards and a hypotenuse of 13 yards, the missing leg measures approximately 12 yards.