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

36 miles. Call Fort Collins point F, Cheyenne, point C, and Laramie point L. We know that angle F=46.5 degrees, angle L=43.6 degrees, and FC=3.2 inches. Use the law of sines, sinF/LC=sinL/FC,  LC=sin46.5*3.2/sin43.6=2.32/0.69=3.36 inches. Since one inch represents 10.6 miles, 3.36 inches is 36 miles, the distance from L to C.