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:
[tex]\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}[/tex]
We solve the equation for the value of angle C:
[tex]\begin{gathered} \cos C=0.1642 \\ C=\arccos (0.1642) \\ C=80.55\degree\approx80.6\degree \end{gathered}[/tex]
Recall that Orlando is due South of Niagara Falls.
Thus, the bearing of Denver from Niagara Falls is S80.6°W.
