Question

find the unknown length in the right triangle shown to the right. 39 in. 80 in. the unknown length in the given right triangle is 89 (type a whole number or decimal rounded to the near) inches. inches cubed. square inches.

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, \(a = 39\) in, \(b = 80\) in, and \(c\) is the unknown.

Step2: Substitute values

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

Step3: Solve for \(c\)

Take the square root of both sides: \(c = \sqrt{7921} = 89\). The unit for length is inches, so we choose "inches".

Answer:

inches