Question

Round your answers to five significant digits. Write your answers for angle measures in decimal degrees.

Answer 1

We will have the following:

We first determine "b", that is:

`\begin{gathered} b=√(42766^2-35276^2)\Rightarrow b=24177.14996... \\ \\ \Rightarrow b\approx24177 \end{gathered}`

Now, using the law of sines we determine the measure of the angles, that is:

alpha:

`\begin{gathered} (sin(\alpha))/(35276)=(sin(90))/(42766)\Rightarrow sin(\alpha)=(35276)/(42766) \\ \\ \Rightarrow\alpha=sin^(-1)((35276)/(42766))\Rightarrow\alpha=55.5743883... \\ \\ \Rightarrow\alpha\approx55.574 \end{gathered}`

Beta:

`\begin{gathered} (sin(\beta))/(24177.14996)=(sin(90))/(42766)\Rightarrow sin(\beta)=(24177.14996)/(42766) \\ \\ \Rightarrow\beta=sin^(-1)((24177.14996)/(42766))\Rightarrow\beta=34.42561171... \\ \\ \Rightarrow\beta\approx34.426 \end{gathered}`