In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the lengt

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Question: In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Options:

Correct Answer: 8

Solution:

Using the Pythagorean theorem, b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Step 1: Identify the parts of the right triangle. The hypotenuse (longest side) is 10, and one leg (shorter side) is 6.
Step 2: Recall the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse and a and b are the legs.
Step 3: In our case, we know c (the hypotenuse) is 10 and one leg (a) is 6. We need to find the other leg (b).
Step 4: Rearrange the Pythagorean theorem to find b: b² = c² - a².
Step 5: Substitute the known values into the equation: b² = 10² - 6².
Step 6: Calculate 10², which is 100, and 6², which is 36.
Step 7: Now, subtract 36 from 100: 100 - 36 = 64.
Step 8: To find b, take the square root of 64: b = √64.
Step 9: Calculate the square root of 64, which is 8.
Step 10: Therefore, the length of the other leg is 8.

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), expressed as c² = a² + b².