Question

The information given represents lengths of sides of a right triangle with c as the hypotenuse. What is the correct missing length, c, to the nearest hundredth? A calculator may be helpful. a = 16, b = 28, ​c = ?

Options:
Option 1: 31.46
Option 2: 31.94
Option 3: 32.09
Option 4: 32.25

Answer 1

The Pythagorean theorem is applied by squaring the given lengths of the sides and then taking the square root of their sum to find the hypotenuse. For a right triangle with sides a = 16 and b = 28, the hypotenuse is approximately 32.25, making option 4 the correct answer.

Step-by-step explanation:

The student has provided the lengths of two sides of a right triangle and is seeking the length of the hypotenuse, labeled c. The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (labeled a and b), can be used to solve this problem: a² + b² = c². This formula can be rewritten to solve for c: c = √(a² + b²).

In this case, we plug in the values a = 16 and b = 28 into the formula:

c = √(16² + 28²)
c = √(256 + 784)
c = √1040
c ≈ 32.25

Therefore, the length of the hypotenuse c, to the nearest hundredth, is approximately 32.25.