What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)

Rationale

The length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet is approximately 8.9 feet.

This length was found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can use this theorem to find the unknown leg's length by subtracting the square of the known leg from the square of the hypotenuse, and then taking the square root of the result.

A (40 feet) YOUR ANSWER

This answer is incorrect because it significantly exceeds the length of the hypotenuse. In a right triangle, the hypotenuse is always the longest side. If the unknown leg were 40 feet, this would make it longer than the hypotenuse, which contradicts the properties of a right triangle.

B (4 feet) YOUR ANSWER

This answer is incorrect. By using the Pythagorean theorem, the square of the hypotenuse (144 square feet) minus the square of the known leg (64 square feet) equals 80 square feet. The square root of 80 is approximately 8.9, not 4 feet.

C (14.4 feet) YOUR ANSWER

This answer is incorrect because it also exceeds the length of the hypotenuse. The hypotenuse is always the longest side in a right triangle, so the length of the unknown leg cannot be greater than that of the hypotenuse.

D (8.9 feet) CORRECT

This is the correct answer. Using the Pythagorean theorem, the square of the hypotenuse (144 square feet) minus the square of the known leg (64 square feet) equals 80 square feet. The square root of 80 is approximately 8.9 feet, which is the length of the unknown leg.

Conclusion

The Pythagorean theorem allows us to calculate the length of the unknown leg in a right triangle if we know the lengths of the other two sides. In this case, the unknown leg is approximately 8.9 feet, making choice D the correct answer. The other options are inconsistent with the properties of a right triangle and the application of the Pythagorean theorem.

What is the length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth)

The length of the unknown leg of a right triangle that has one leg measuring 8 feet and a hypotenuse of 12 feet is approximately 8.9 feet.

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