Question

refer to the right triangle. find c if a = 42 and b = 40. c = enter an exact number. suggested tutorial: learn it: simplify a radical expression. resources read it

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \(c^2 = a^2 + b^2\), where \(a = 42\) and \(b = 40\). So we substitute the values: \(c^2=42^2 + 40^2\)

Step2: Calculate the squares

\(42^2 = 1764\) and \(40^2=1600\). Then \(c^2=1764 + 1600=3364\)

Step3: Take the square root

To find \(c\), we take the square root of \(3364\). Since \(58\times58 = 3364\), so \(c=\sqrt{3364}=58\)

Answer:

\(58\)