Question

1. solve for the unknown variable for a right triangle:

a = 5in, b = 4in, c = ____ (triangle image)
remember to show all work.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(a = 5\) in, \(b = 4\) in.

Step2: Substitute values into formula

\(c^2 = 5^2 + 4^2 = 25 + 16\)

Step3: Calculate and take square root

\(c^2 = 41\), so \(c = \sqrt{41} \approx 6.403\) in.

Answer:

\(c=\sqrt{41}\) inches (or approximately \(6.40\) inches)