Introduction to Finding the Length of AB in a Right Triangle

Have you ever wondered how to find the length of the side AB when given the lengths of the other two sides in a right triangle? This guide will walk you through the process using the Pythagorean theorem, ensuring your content is optimized for Google search results.

Understanding the Pythagorean Theorem

The Pythagorean theorem is a cornerstone in geometry, used to find the length of the sides of a right triangle. The theorem states that in a right triangle, 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. This can be expressed as:

AB2 AC2 BC2

Step-by-Step Process to Find the Length of AB

Identify the Given Values: In this case, we are given AC 5 cm and BC 12 cm. We need to find the length of AB, assuming that the triangle is a right triangle with right angle at C. Apply the Pythagorean Theorem: Plugging in the values, we get: Calculation: Option 1 (BC as the Hypotenuse): BC is the hypotenuse, so: AB2 AC2 - BC2 (since the hypotenuse is the square root of the sum of the squares of the other two sides) AB2 52 - 122 This leads to AB2 25 - 144, which results in a negative number, which is not possible in the real world. Hence, BC cannot be the hypotenuse in this case. Option 2 (BC as a Leg): Since BC is not the hypotenuse, it must be a leg of the triangle. Therefore, we can use: AB2 AC2 BC2 AB2 52 122 AB2 25 144 AB2 169 Taking the square root of both sides, we get: AB √169 13 cm

Conclusion and Further Reading

Therefore, given the lengths AC 5 cm and BC 12 cm, the length of AB is 13 cm, assuming the triangle is a right triangle. For more detailed information on right triangles and the Pythagorean theorem, check out the following resources:

Right triangle properties Pythagorean theorem applications

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