Question

what is the approximate distance from one corner of the soccer field to the opposite corner? 180 yards 117 yards 80 yards 130 yards 60 yards

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). The length and width of the soccer field form the two legs of a right - triangle, and the diagonal (distance between opposite corners) is the hypotenuse. Here, \(a = 100\) yards and \(b=60\) yards.

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(a^{2}=100^{2}=10000\) and \(b^{2}=60^{2}=3600\).

Step3: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=10000 + 3600=13600\).

Step4: Calculate the square - root

\(c=\sqrt{13600}\approx116.62\approx117\) yards.

Answer:

117 yards