College Math Placement Practice Test

What is the result of calculating the value of c using the Pythagorean Theorem for legs of 50 feet and 80 feet?

1. 80 feet

2. 85 feet

3. 89 feet

4. 94 feet

The correct answer is: 94 feet

To determine the length of the hypotenuse \( c \) using the Pythagorean Theorem, you can apply the formula: \[ c = \sqrt{a^2 + b^2} \] where \( a \) and \( b \) are the lengths of the two legs of the right triangle. In this case, the legs are given as 50 feet and 80 feet. First, calculate \( a^2 \) and \( b^2 \): \[ 50^2 = 2500 \] \[ 80^2 = 6400 \] Next, add these two values together: \[ 2500 + 6400 = 8900 \] Now, take the square root of this sum to find \( c \): \[ c = \sqrt{8900} \] Calculating the square root gives: \[ c \approx 94.34 \] Since the choices provided are rounded values, the closest value is approximately 94 feet, confirming the correctness of that answer. The other options do not reflect the accurate calculation based on the Pythagorean Theorem, hence they do not match the expected value derived from the equation.