Question

find the missing side of each triangle. round your answers to the nearest tenth if necessary

Explanation:

Step1: Apply Pythagorean theorem for (17)

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 5\), \(b\) is unknown, \(c=13\). Let \(x\) be the unknown side. Then \(x^{2}+5^{2}=13^{2}\), so \(x^{2}=13^{2}-5^{2}\).

Step2: Calculate \(x\) for (17)

\(x^{2}=169 - 25=144\), then \(x=\sqrt{144}=12\) cm.

Step3: Apply Pythagorean theorem for (18)

For a right - triangle with legs \(a = 6\) and \(b = 8\), and hypotenuse \(x\). Using \(a^{2}+b^{2}=x^{2}\), so \(x^{2}=6^{2}+8^{2}\).

Step4: Calculate \(x\) for (18)

\(x^{2}=36 + 64=100\), then \(x=\sqrt{100}=10\) m.

Step5: Apply Pythagorean theorem for (19)

For a right - triangle with legs \(x\) and \(9\), and hypotenuse \(15\). Using \(x^{2}+9^{2}=15^{2}\), so \(x^{2}=15^{2}-9^{2}\).

Step6: Calculate \(x\) for (19)

\(x^{2}=225-81 = 144\), then \(x=\sqrt{144}=12\) cm.

Answer:

1. \(12\) cm; 18) \(10\) m; 19) \(12\) cm