Question

April works as a courier delivering and picking up packages for a shipping company. Three of the communities on her route form an isosceles right triangle as shown in the figure. There are approximately 48 miles between Old Mill and Clarksville and between Clarksville and Hamilton. Approximately how many miles are there between Old Mill and Hamilton? Round your answer to the nearest mile if necessary.

Answer 1

Because the route forms an isosceles right triangle, two legs of the triangle are equal.
There will be two angles, equal to 45°, and a 90° angle as shown in the figure below.

The distance from Old Mill is the same as the distance from Clarksville to Hamilton, equal to 48 miles.

Let x =  distance between Old Mill and Hamilton.
By definition, 
cos 45° = 48/x
or 
x = 48/cos 45° = 67.882 mi

Answer: 68 miles (nearest mile)