Question

1. solve for the unknown variable for a right triangle: a = 5in, b = 4in, c = ___

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, \(a = 50\), \(b = 40\), and we need to find \(c\).

Step2: Substitute the values

Substitute \(a = 50\) and \(b = 40\) into the formula: \(50^2 + 40^2 = c^2\)

Step3: Calculate the squares

\(50^2 = 2500\) and \(40^2 = 1600\), so \(2500 + 1600 = c^2\)

Step4: Sum the values

\(2500 + 1600 = 4100\), so \(c^2 = 4100\)

Step5: Take the square root

\(c = \sqrt{4100}\)

Step6: Simplify the square root

\(\sqrt{4100} = \sqrt{100\times41} = 10\sqrt{41} \approx 64.03\) (if we want a decimal approximation)

Answer:

If we want the exact form, \(c = 10\sqrt{41}\); if we want the approximate decimal form, \(c \approx 64.03\)