Use the Pythagorean theorem to find the missing side of the...

Use the Pythagorean theorem to find the missing side of the right triangle with legs a and $b$ and hypotenuse $c .$ Then calculate the perimeter. Approximate values to the nearest tenth when appropriate.
Hypotenuse 10 inches and leg 6 inches

Key Concepts

Approximation

In many mathematical problems, particularly those involving irrational numbers, it is common to approximate values to a certain degree of precision (for example, to the nearest tenth). Approximation allows for the presentation of a simplified or more easily interpreted numerical answer, while still maintaining reasonable accuracy.

Perimeter Calculation

The perimeter of any polygon, including a triangle, is the total distance around the shape. For a triangle, the perimeter is calculated by adding together the lengths of all three sides. This concept is essential in many areas of geometry and practical applications, such as construction and land measurement.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in Euclidean geometry that relates the lengths of the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which are known as the legs. This theorem is widely used to determine a missing side length when the other two side lengths are known.

Right Triangle Properties

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. The side opposite this right angle is the hypotenuse, the longest side of the triangle, while the other two sides are referred to as the legs. The unique properties of right triangles allow for the use of the Pythagorean Theorem to solve for unknown side lengths.

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