A right triangle has one leg of length 9 and a hypotenuse of length 15. What is

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

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

Step 1: Identify the lengths given in the problem. One leg (a) is 9 and the hypotenuse (c) is 15.
Step 2: Recall the Pythagorean theorem, which states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse.
Step 3: Rearrange the formula to find the length of the other leg (b). The formula becomes b² = c² - a².
Step 4: Substitute the known values into the formula. Here, c = 15 and a = 9, so we have b² = 15² - 9².
Step 5: Calculate 15², which is 225, and 9², which is 81.
Step 6: Subtract 81 from 225 to find b²: 225 - 81 = 144.
Step 7: Take the square root of 144 to find b: √144 = 12.
Step 8: Conclude that 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).