Question

math 003. fall 2025
acheley abraham-abraham 09/06/25 12:20 pm
it 3 - geometry
question 43, 6.6.35
hw score: 89.66%, 52 of 58 points
points: 0 of 1
find the unknown length in the right triangle shown to the right.
72 mm
30 mm
the unknown length in the given right triangle is
(type a whole number or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = 72\) mm, \(b = 30\) mm, and we need to find \(c\).

Step2: Substitute the values

Substitute \(a = 72\) and \(b = 30\) into the formula: \(c^2 = 72^2 + 30^2\).
Calculate \(72^2 = 5184\) and \(30^2 = 900\). Then \(c^2 = 5184 + 900 = 6084\).

Step3: Solve for \(c\)

Take the square root of \(6084\): \(c = \sqrt{6084} = 78\).

Answer:

78