In a right triangle, if the lengths of the legs are 8 and 15, what is the length

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Question: In a right triangle, if the lengths of the legs are 8 and 15, what is the length of the hypotenuse?

Options:

Correct Answer: 17

Solution:

Using the Pythagorean theorem, c = √(8² + 15²) = √(64 + 225) = √289 = 17.

In a right triangle, if the lengths of the legs are 8 and 15, what is the length of the hypotenuse?

In a right triangle, if the lengths of the legs are 8 and 15, what is the length of the hypotenuse?

Step 1: Identify the lengths of the legs of the right triangle. Here, the lengths are 8 and 15.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as c² = a² + b².
Step 3: Substitute the lengths of the legs into the formula. Here, a = 8 and b = 15, so we have c² = 8² + 15².
Step 4: Calculate the squares of the legs. 8² = 64 and 15² = 225.
Step 5: Add the squares together. 64 + 225 = 289.
Step 6: To find the length of the hypotenuse (c), take the square root of 289. This means c = √289.
Step 7: Calculate the square root of 289, which is 17. Therefore, the length of the hypotenuse is 17.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as c² = a² + b².