Question

On a map, Orlando is 187 millimeters due south of Niagara Falls, Denver is 282 millimetersfrom Orlando, and Denver is 244 millimeters from Niagara Falls (see figure). Find the bearingof Denver from Niagara Falls.Niagara FallsDenverOrlando

Answer 1

Answer:

S80.6°W

Explanation:

From the diagram:

• Niagara Falls to Denver, a = 244 millimeters

,

• Niagara Falls to Orlando, b = 187 millimeters

,

• Denver to Orlando, c = 282 millimeters

To find the bearing of Denver from Niagra falls, the first thing is to find the angle at Niagra Falls(C) using the Law of Cosines.

Angle C is opposite side c.

From the law of cosines:

$\begin{gathered} \cos C=\frac{a^2+b^2-c^2}{2ab} \\ \implies\cos C=\frac{244^2+187^2-282^2}{2\mleft(244\mright)\mleft(187\mright)} \end{gathered}$

We solve the equation for the value of angle C:

$\begin{gathered} \cos C=0.1642 \\ C=\arccos (0.1642) \\ C=80.55\degree\approx80.6\degree \end{gathered}$

Recall that Orlando is due South of Niagara Falls.

Thus, the bearing of Denver from Niagara Falls is S80.6°W.