When you think of the situation as a whole, you may notice that the lines in the problem actually form a triangle. First, the man driving 10 miles east forms a bottom leg of the triangle 10 units long. When he drives the 2 miles north, he adds another leg of 2 units length. When the place of work is connected to the starting position through a line, a third and final line is drawn which creates the triangle.
So, how can we find the direct distance from his place of work to his home? We can use the Pythagorean Theorem (, where
and
are the lengths of the legs of the triangle and
is the length of the hypotenuse). We know that the lengths of the legs are 10 and 2, which we can use in the formula, as shown below:
Now, we can solve this equation for :
The distance would be √104 miles, or approximately 10.2 miles.