Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth
c = \boxed{} meters
(with a right triangle diagram labeled 72 m, 54 m, and hypotenuse c)

Explanation:

Step1: Identify the formula

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 72\), \(b = 54\), and \(c\) is the hypotenuse.

Step2: Substitute the values

Substitute \(a = 72\) and \(b = 54\) into the formula: \(72^2 + 54^2 = c^2\)
Calculate \(72^2 = 5184\) and \(54^2 = 2916\)
Then \(5184 + 2916 = c^2\)

Step3: Simplify the left side

\(5184 + 2916 = 8100\), so \(c^2 = 8100\)

Step4: Solve for \(c\)

Take the square root of both sides: \(c = \sqrt{8100} = 90\)

Answer:

90