A right triangle has one leg measuring 9 and the hypotenuse measuring 15. What i

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Question: A right triangle has one leg measuring 9 and the hypotenuse measuring 15. What is the length of the other leg?

Options:

Correct Answer: 12

Solution:

Using the Pythagorean theorem, b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12.

A right triangle has one leg measuring 9 and the hypotenuse measuring 15. What is the length of the other leg?

A right triangle has one leg measuring 9 and the hypotenuse measuring 15. What is the length of the other leg?

Step 1: Identify the sides of the right triangle. We have one leg (a) measuring 9 and the hypotenuse (c) measuring 15.
Step 2: Recall the Pythagorean theorem, which states that a² + b² = c², where a and b are the legs and c is the hypotenuse.
Step 3: Rearrange the formula to find the length of the other leg (b): b = √(c² - a²).
Step 4: Substitute the values into the formula: b = √(15² - 9²).
Step 5: Calculate 15², which is 225.
Step 6: Calculate 9², which is 81.
Step 7: Subtract 81 from 225: 225 - 81 = 144.
Step 8: Take the square root of 144: √144 = 12.
Step 9: Therefore, the length of the other leg is 12.

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 legs (a and b).