1. What is the length of the hypotenuse of a right triangle with legs of length 80 feet and 150 feet? Show
all algebraic work for full credit.

Answer:

80^2 + 150^2

6400 + 22500 = 28,900

Something squared will equal 28,900

170^2 = 28,900

170 is your answer!

The length of the hypotenuse of the right triangle with legs of 80 feet and 150 feet is 170 feet.

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In this case, the legs of the triangle have lengths of 80 feet and 150 feet, so we can label them as follows:

Leg 1: a = 80 feet

Leg 2: b = 150 feet

We can then use the Pythagorean theorem to solve for the length of the hypotenuse, which we can label as c:

c² = a² + b²

Substituting in the values for a and b, we get:

c² = (80 feet)² + (150 feet)²

c² = 6,400 square feet + 22,500 square feet

c² = 28,900 square feet

c = √(28,900 square feet)

c = 170 feet

Therefore, the length of the hypotenuse of the right triangle with legs of 80 feet and 150 feet is 170 feet.

Learn more about the Pythagorean theorem here:

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