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 sides X, X plus 1, and X minus 7. And we're asked to find the

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

Key Concepts

Algebraic Manipulation

Algebraic manipulation is involved in solving equations that arise from applying the Pythagorean theorem. This includes techniques such as isolating variables, taking square roots, and rearranging terms to solve for the unknown side lengths of a triangle.

Hypotenuse and Legs

In a right triangle, the hypotenuse is the longest side and is always opposite the right angle, while the other two sides are referred to as the legs. Recognizing the hypotenuse and the legs is essential when applying the Pythagorean theorem to determine unknown side lengths.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in Euclidean geometry that applies to right triangles. It states that the sum of the squares of the two legs (the sides adjacent to the right angle) is equal to the square of the hypotenuse (the side opposite the right angle), typically expressed as a^2 + b^2 = c^2.

Right Triangle

A right triangle is a triangle that includes one 90-degree angle. Understanding the properties of a right triangle is crucial because specific relationships, such as the relationship between its sides, only hold when one of the angles is exactly 90 degrees.

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