Answer:
Number of distinct triangles = 1
Step-by-step explanation:
We have sine rule [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex].
Here given c=3, b=5 and B=85 degrees
Substituting
[tex]\frac{5}{sin85}=\frac{3}{sinC}\\\\sinC=0.598\\\\C=36.71^0[/tex]
We also have
A+B+C = 180°
A+85+36.71 = 180
A = 58.29°
Substituting in sine rule.
[tex]\frac{5}{sin85}=\frac{a}{sin58.29}\\\\a=4.27[/tex]
Triangle is given by
a = 4.27, b= 5 , c= 3, A = 58.29°, B= 85° and C = 36.71°.
Only this combination is possible.
Number of distinct triangles = 1
