Question

Can someone show the work?

Answer 1

Check the picture below.

`\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{a}{\sin(43^o)}=\cfrac{18}{\sin(71^o)}\implies a\sin(71^o)=18\sin(43^o) \\\\\\ a=\cfrac{18\sin(43^o)}{\sin(71^o)}\implies a\approx 12.98 \\\\[-0.35em] ~\dotfill`

`\cfrac{c}{\sin(66^o)}=\cfrac{18}{\sin(71^o)}\implies c\sin(71^o)=18\sin(66^o) \\\\\\ c=\cfrac{18\sin(66^o)}{\sin(71^o)}\implies c\approx 17.39`

Make sure your calculator is in Degree mode.

Answer 2

You can use the rule of sines to work this one out. a/sinA = b/sinB = c/sinC

The calculations and steps I took are all in the attached screenshots. I hope this helps!

The answers I got were ∠B=71º, a=12.89 and c=17.24