Using the definitions of cosine and tangent:
[tex]\begin{gathered} \cos A=\frac{b}{c}\Rightarrow c=\frac{b}{\cos A}...(1) \\ \\ \tan A=\frac{a}{b}\Rightarrow a=b\cdot\tan A...(2) \end{gathered}[/tex]
From the problem, we identify:
[tex]\begin{gathered} A=26\degree \\ b=7 \end{gathered}[/tex]
We use these values to find a and c.
In (1):
[tex]c=\frac{7}{\cos26\degree}\approx7.788[/tex]
In (2):
[tex]a=7\cdot\tan26\degree\approx3.414[/tex]
Answer:
a = 3.414
b = 7.788
