Question

find the unknown length in the right triangle shown to the right. the unknown length in the given right triangle is (type a whole number or decimal rounded to the nea s needed.)

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c = \sqrt{a^{2}+b^{2}}\) (or if we are finding a leg, \(a=\sqrt{c^{2}-b^{2}}\), but here we need the hypotenuse since the unknown side is opposite the right angle). Let \(a = 72\) mm and \(b=30\) mm.

Step2: Substitute values into the formula

First, calculate \(a^{2}\) and \(b^{2}\).
\(a^{2}=72^{2}=72\times72 = 5184\)
\(b^{2}=30^{2}=30\times30=900\)
Then, add them together: \(a^{2}+b^{2}=5184 + 900=6084\)

Step3: Take the square root

Now, find the square root of \(6084\) to get the hypotenuse \(c\).
\(c=\sqrt{6084}=78\)

Answer:

78 mm