Question

find the missing side length (include units). round to the nearest hundredth, if necessary. 21 mi 28 mi x

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, let \(a = 21\) mi, \(b=x\), and \(c = 28\) mi. Then \(x^{2}+21^{2}=28^{2}\).

Step2: Rearrange the equation

We can rewrite it as \(x^{2}=28^{2}-21^{2}\). Calculate \(28^{2}=784\) and \(21^{2}=441\). So \(x^{2}=784 - 441=343\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{343}\approx18.52\) mi.

Answer:

\(18.52\) mi