Question

Examples of calculating the hypotenuse of a right triangle using the Pythagorean theorem:

Example 1:
Given the lengths of the two legs of a right triangle as a = 3 and b = 4, we can calculate the hypotenuse (c) using the formula:
c² = a² + b²

Answer 1

Certainly! The Pythagorean theorem is a formula that relates to the three sides of a right triangle. Specifically, it states that the sum of the squares of the two shorter sides (also known as the legs) is equal to the square of the longest side, which is called the hypotenuse. Here are the steps to find the length of the hypotenuse given the lengths of the two legs:

Identify the two legs of the right triangle.

Square each of the leg lengths.

Add the two squared leg lengths together.

Take the square root of the sum from step 3.

The resulting value will be the length of the hypotenuse. For example, if the two legs of a right triangle have lengths of 3 and 4, respectively, then the hypotenuse length can be found as follows:

The two legs are 3 and 4.

Squaring each of these values gives 9 and 16.

Adding these squared values together gives 25.

Taking the square root of 25 gives 5.

Therefore, the length of the hypotenuse in this triangle is 5.

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Explanation:

Answer 2

c = 5

Explanation:

using the formula to calculate the hypotenuse c

c² = a² + b² ( substitute a = 3 and b = 4 into the formula )

c² = 3² + 4² = 9 + 16 = 25 ( take square root of both sides )

`√(c^2)` =
`√(25)` , then

c = 5