Question

What is the answer to the question

Answer 1

From the right triangle, and using the definitions of the tangent and the cosine functions, we have:

`\begin{gathered} \tan B=(AC)/(BC)=(b)/(a)\Rightarrow b=a\cdot\tan B...(1) \\ \\ \cos B=(BC)/(AB)=(a)/(c)\Rightarrow c=(a)/(\cos B)...(2) \end{gathered}`

From the problem, we identify:

`\begin{gathered} B=55.7\degree \\ a=266\text{ km} \end{gathered}`

Finally, using these values, we can find b and c.

Using (1):

`\begin{gathered} b=266\cdot\tan55.7\degree \\ \\ \therefore b=389.941\text{ km} \end{gathered}`

Using (2):

`\begin{gathered} c=(266)/(\cos55.7\degree) \\ \\ \therefore c=472.028\text{ km} \end{gathered}`