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:

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

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):

$c=\frac{7}{\cos26\degree}\approx7.788$

In (2):

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

Answer:

a = 3.414

b = 7.788