Question

multiple choice show all work for credit. identify the choice that best completes the statement or answers the question. find the length of the missing side. (the triangle is not drawn to scale.) 1. a. 28 b. 100 c. 10 d. 48 2. a. 35 b. 49 c. 7 d. 2 find the length of the missing side. leave your answer in simplest radical form. 3. not drawn to scale a. \\( \sqrt { 1 7 } \\) m b. 113 m c. \\( \sqrt { 1 1 3 } \\) m d \\( \sqrt { 7 1 } \\) 4. not drawn to scale a. \\( \sqrt { 2 1 8 } \\) cm b. \\( 2 \sqrt { 5 } \\) cm c. \\( \sqrt { 6 } \\) cm d \\( 2 \sqrt { 3 0 } \\)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).

Step2: Solve for the missing side in problem 3

Let \(a = 7\) and \(b = 8\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{7^{2}+8^{2}}=\sqrt{49 + 64}=\sqrt{113}\)

Answer:

c. \(\sqrt{113}\) m