Question

directions use the pythagorean theorem and a calculator to find the missing side of each triangle. round to the nearest tenth. 1) a = 2 b = 7 c = \square

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\) (assuming \(c\) is the hypotenuse). Given \(a = 2\) and \(b=7\), we substitute these values into the formula.

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(a^{2}=2^{2} = 4\) and \(b^{2}=7^{2}=49\).

Step3: Find \(c^{2}\)

\(c^{2}=a^{2}+b^{2}=4 + 49=53\).

Step4: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{53}\). Using a calculator, \(\sqrt{53}\approx7.3\) (rounded to the nearest tenth).

Answer:

\(7.3\)