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 nearest thousandth as needed.)

Explanation:

Step1: Identify the formula

We use the Pythagorean theorem for a right triangle, which is \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = 39\) in, \(b = 80\) in, and we need to find \(c\).

Step2: Substitute the values

Substitute \(a = 39\) and \(b = 80\) into the formula: \(c^2 = 39^2 + 80^2\).
Calculate \(39^2 = 1521\) and \(80^2 = 6400\). Then \(c^2 = 1521 + 6400 = 7921\).

Step3: Solve for \(c\)

Take the square root of \(7921\): \(c=\sqrt{7921}=89\).

Answer:

89