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

₹0.0

Question: If the lengths of the legs of a right triangle 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.

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

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

Step 1: Identify the lengths of the legs of the right triangle. Here, one leg is 8 and the other leg is 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.
Step 8: 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).