We have the following triangle:
First, we start from the fact that we have an internal angle of 72 degrees and a right angle i.e. a 90-degree angle.
Second, having two internal angles, we solve and find the last internal angle.
[tex]180-90-72=18[/tex]
Third, we find "a" and "b" with the law of sines, the equation of this law is:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}=\frac{c}{sn(C)}[/tex]
Where we have these values:
[tex]\begin{gathered} a=a \\ b=b \\ c=11 \\ \sin (A)=\sin (18) \\ \sin (B)=\sin (72) \\ \sin (C)=\sin (90)=1 \end{gathered}[/tex]
Now we solve "a"
[tex]\begin{gathered} \frac{a}{\sin (18)}=\frac{11}{\sin (90)} \\ a=11\cdot\sin (18) \\ a=3.3991\cong3.4 \end{gathered}[/tex]
Now we solve "b"
[tex]\begin{gathered} \frac{b}{\sin (72)}=\frac{11}{\sin (90)} \\ b=11\cdot\sin (72) \\ b=10.4646\cong10.46 \end{gathered}[/tex]
In conclusion, the answers are approximate:
[tex]\begin{gathered} a\cong3.4 \\ b\cong10.46 \end{gathered}[/tex]
