Question

9 find the missing side of the triangle. round to the nearest tenth. 8 mi 16 mi x

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let \(a = 8\), \(c=16\), and \(b=x\). Then \(x^{2}+8^{2}=16^{2}\).

Step2: Simplify the equation

\(x^{2}+64 = 256\). Subtract 64 from both sides: \(x^{2}=256 - 64\). So \(x^{2}=192\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{192}\). Since \(\sqrt{192}=\sqrt{64\times3}=8\sqrt{3}\approx8\times1.732 = 13.856\).

Answer:

\(13.9\) mi