Question

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

Answer 1

Answer : Distance from Cheyenne to Laramie = 36 miles .

Explanation :

Since we have given that

Distance from Fort Collins to Cheyenne =3.2 inches

Angle formed at Laramie =
`43.6\textdegree`

Angle formed at Fort Collins =
`46.5\textdegree`

Since we have drawn our figure mentioning the cordinates as L,F, C where L represents Laramie, F represents Fort Collins and C represents Cheyenne

Now, we use the cosine- sine formula which is given by

`(\sin(A))/(A)=(\sin(B))/(B)`

`(sin(43.6\textdegree))/(3.2)=(sin (46.5\textdegree))/(x)\\\\(0.689619543)/(3.2)=(0.725374371)/(x)\\\\`

`\text{ By cross multiplication, we get}\\\\x=(2.32)/(0.69)\\\\x=3.36\text{ inches}`

Now, we will change it into miles ,

`\text{ So ,Distance from Cheyenne to Laramie }=3.36* 10.6=35.616`

But we want it in nearest whole mile ,

So, distance from Cheyenne to Laramie = 36 miles .

Answer 2

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.