On a map the distance from fort collins to cheyenne is 3.2 inches. the angle formed at laramie has measure 43.6º, and the angle formed at fort collins has measure 46.5º. if one inch on the map is equal to 10.6 miles, find the distance from cheyenne to laramie to the nearest whole mile

We can solve this by drawing a triangle with three points. The first point at Fort Collins (F), the second at Cheyenne (C) and the third at Laramie (L).

The angle at F = 46.5, the angle at L = 43.6. We know the side opposite angle L = 3.2 (side FC), now we must solve for the side opposite angle F (side LC).

We can use the law of sines to solve this where:

sinA/a = sinB/b
sin43.6/ 3.2 = sin46.5/LC
LC = 3.2 (sin46.5/sin43.6)
LC = 3.37 inches

We are told 1 in = 10.6 miles, therefore:

3.37 inches x 10.6 miles/in = 36 miles from Laramie to Cheyenne.