Question

Note: Triangle may not be drawn to scale. Suppose A = 26 degrees and b = 7

Answer 1

Using the definitions of cosine and tangent:

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

From the problem, we identify:

`\begin{gathered} A=26\degree \\ b=7 \end{gathered}`

We use these values to find a and c.

In (1):

`c=(7)/(\cos26\degree)\approx7.788`

In (2):

`a=7\cdot\tan26\degree\approx3.414`

Answer:

a = 3.414

b = 7.788