Question

mj lives 80 miles north of the capital and his brother pj lives 39 miles east of the capital. find the distance between mjs house and pjs house.

Explanation:

Step1: Identify right - triangle

The positions of MJ, PJ and the capital form a right - triangle, with the distances from MJ and PJ to the capital as the two legs.

Step2: Apply Pythagorean theorem

Let \(a = 80\) (distance of MJ from capital) and \(b = 39\) (distance of PJ from capital). The distance \(d\) between MJ and PJ is given by \(d=\sqrt{a^{2}+b^{2}}\), so \(d=\sqrt{80^{2}+39^{2}}=\sqrt{6400 + 1521}=\sqrt{7921}\).

Step3: Calculate the square - root

\(\sqrt{7921}=89\).

Answer:

89 miles