Question

find the missing side of each 1) 6 km $sqrt{37}$ km x

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, if the two legs of the right - triangle are \(a = 6\) and \(b\), and the hypotenuse \(c=\sqrt{37}\), we can find the other leg. Let the unknown leg be \(b\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

Substitute \(a = 6\) and \(c=\sqrt{37}\) into the formula \(b^{2}=c^{2}-a^{2}\). We get \(b^{2}=(\sqrt{37})^{2}-6^{2}\). Since \((\sqrt{37})^{2}=37\) and \(6^{2}=36\), then \(b^{2}=37 - 36=1\).

Step3: Solve for \(b\)

Taking the square root of both sides of \(b^{2}=1\), we have \(b = 1\) (we take the positive value since length cannot be negative).

Answer:

\(1\) km