Chapter 6.2, Problem 50E

a.

To determine

The bearing of the Minneapolis from the Phoenix.

Answer to Problem 50E

The answer is N59.7^oE.

Explanation of Solution

Given:

The diagram is given as:

  

Considering the given diagram, where M is Minneapolis, P is phoenix and A is Albany:

  

From the cosine rule:

  $\begin{array}{l}\cos M=\frac{{216}^2+{165}^2-{368}^2}{2\left(216\right)\left(165\right)}\\ =-\frac{61543}{71280}\\ =-{0.86}^o\\ M=\cos \left(-{0.86}^o\right)\\ M={30.3}^o\end{array}$

Hence, the bearing of the Minneapolis from the Phoenix is:

  $90-30.3={59.70}^0$

Therefore, the answer is N59.7^oE.

b.

To determine

The bearing of the Albany from the Phoenix.

Answer to Problem 50E

The answer is N72.8^o E.

Explanation of Solution

Given:

The diagram is given as:

  

Considering the given diagram, where M is Minneapolis, P is phoenix and A is Albany:

  

From the cosine rule:

  $\begin{array}{l}\cos A=\frac{{368}^2+{165}^2-{216}^2}{2\left(368\right)\left(165\right)}\\ =\frac{115993}{121440}\\ =0.955\\ A={17.23}^o\end{array}$

Therefore, the bearing of the Albany from the Phoenix is:

  $\begin{array}{l}90-17.22\\ ={72.77}^o\end{array}$

Therefore, the result is N72.8^o E