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Ghella [55]
3 years ago
6

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

Mathematics
2 answers:
juin [17]3 years ago
8 0
36 miles. Call <span>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. </span>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.
Debora [2.8K]3 years ago
3 0

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

\frac{\sin(A)}{A}=\frac{\sin(B)}{B}

\frac{sin(43.6\textdegree)}{3.2}=\frac{sin (46.5\textdegree)}{x}\\\\\frac{0.689619543}{3.2}=\frac{0.725374371}{x}\\\\

\text{ By cross multiplication, we get}\\\\x=\frac{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\times 10.6=35.616

But we want it in nearest whole mile ,

So, distance from Cheyenne to Laramie = 36 miles .


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