Find the lengths of the sides of the following right triangles. (Hint: Use the Pythagorean theor

step 1 We're given a right triangle with the side x minus 2, x minus 1, and x. And we're asked to find

Find the lengths of the sides of the following right...

Key Concepts

Right Triangle

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. This property makes it a fundamental object of study in geometry and allows for the application of specific theorems and relationships that do not hold for other types of triangles.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in Euclidean geometry that establishes a relationship between the three sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Hypotenuse

The hypotenuse is the longest side of a right triangle, located directly opposite the right angle. It plays a crucial role in the Pythagorean theorem and solving problems involving right triangles, including finding an unknown side when the other two are known.

Legs

The legs of a right triangle are the two sides that form the right angle. Their lengths, when squared and added together, yield the square of the hypotenuse according to the Pythagorean theorem, making them essential for calculating unknown side lengths.

Algebraic Manipulation

Algebraic manipulation involves rearranging and solving equations to find unknown values. In the context of right triangles, it is used to solve the equation derived from the Pythagorean theorem by isolating the unknown side length and taking square roots as necessary.

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