Answer:
Step-by-step explanation:
In triangle ABC we have[tex]a = 31, c = 42, ∠A = 39°[/tex]
To find other sides and angles.
Use sine formula for triangles
[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sinC} \\\frac{31}{sin39} =\frac{b}{sinB} =\frac{42}{sinc}[/tex]
Cross multiply to get
[tex]Angle C =58.5^{o}[/tex] or [tex]121.5[/tex]
Angle B = 180-A-C
=[tex]82.5^{o}[/tex] or [tex]19.5[/tex]
b =18.84 or 16.44
There are two triangles
with
[tex]Side a = 31\\Side b = 48.84\\Side c = 42\\Angle ∠A = 39° \\Angle ∠B = 82.50° \\Angle ∠C = 58.5°[/tex]
[tex]Side a = 31\\Side b = 16.44204\\Side c = 42\\Angle ∠A = 39° \\Angle ∠B = 19.5° \\Angle ∠C = 121.5°[/tex]
