Question

Two cyclists leave the corner of State Street and Main Street simultaneously. State Street and Main Street are not at right angles; the cyclists' paths have an angle of 135° between them. How far apart are the cyclists after they each travel 3 miles?

Answer 1

5.543 miles

Explanation:

The law of cosines can help with this. It relates side "c" of a triangle to the other two sides (a, b) and the angle between them (C).

c² = a² +b² -2ab·cos(C)

c² = 3² + 3² -2·3·3·cos(135°) = 18(1 -cos(135°)) ≈ 30.7279

c ≈ √30.7279 ≈ 5.543 . . . . miles