The length of the sides of a triangle are given as 8, 15, 17. The hypotenuse is the side that is the length of ____?
c^2 = a^2 + b^2
the hypotenuse is always the longest side.
Thank you Damon. I could not have done this without your help!!
You are welcome :)
To determine which side of the triangle is the hypotenuse, we first need to understand the concept of a right triangle.
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 relationship is known as the Pythagorean theorem.
Using the Pythagorean theorem, we can check which side satisfies the equation:
For a triangle with side lengths 8, 15, and 17:
- Let's assume side A has a length of 8.
- Let's assume side B has a length of 15.
- Let's assume side C has a length of 17.
We can now use the Pythagorean theorem to verify which side is the hypotenuse:
- By substituting the given values into the theorem, we get: 8^2 + 15^2 = 17^2.
- Simplifying, we have: 64 + 225 = 289.
From the equation, we can see that the side with length 17 (side C) is the hypotenuse because it satisfies the Pythagorean theorem.
Therefore, the length of the hypotenuse is 17.