Question

Solve for: A = a b= Round to the nearest tenth.

Answer 1

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.

$180-90-72=18$

Third, we find "a" and "b" with the law of sines, the equation of this law is:

$\frac{a}{\sin(A)}=\frac{b}{\sin (B)}=\frac{c}{sn(C)}$

Where we have these values:

$\begin{gathered} a=a \\ b=b \\ c=11 \\ \sin (A)=\sin (18) \\ \sin (B)=\sin (72) \\ \sin (C)=\sin (90)=1 \end{gathered}$

Now we solve "a"

$\begin{gathered} \frac{a}{\sin (18)}=\frac{11}{\sin (90)} \\ a=11\cdot\sin (18) \\ a=3.3991\cong3.4 \end{gathered}$

Now we solve "b"

$\begin{gathered} \frac{b}{\sin (72)}=\frac{11}{\sin (90)} \\ b=11\cdot\sin (72) \\ b=10.4646\cong10.46 \end{gathered}$

In conclusion, the answers are approximate:

$\begin{gathered} a\cong3.4 \\ b\cong10.46 \end{gathered}$