Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
c = \boxed{} meters

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, \(a = 2\) m, \(b = 7\) m.

Step2: Substitute values

Substitute \(a = 2\) and \(b = 7\) into the formula: \(2^2 + 7^2 = c^2\)

Step3: Calculate squares

\(2^2 = 4\), \(7^2 = 49\), so \(4 + 49 = c^2\)

Step4: Sum the values

\(4 + 49 = 53\), so \(c^2 = 53\)

Step5: Take the square root

\(c = \sqrt{53}\)

Step6: Approximate the value

\(\sqrt{53} \approx 7.3\) (rounded to the nearest tenth)

Answer:

\(7.3\)