Question

Find the number of distinct triangles with c=3, b=5 and B=85 degrees

Answer 1

Answer:

Number of distinct triangles = 1

Step-by-step explanation:

We have sine rule $\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$.

Here given c=3, b=5 and B=85 degrees

Substituting

       $\frac{5}{sin85}=\frac{3}{sinC}\\\\sinC=0.598\\\\C=36.71^0$

We also have

          A+B+C = 180°

          A+85+36.71 = 180

          A = 58.29°

Substituting in sine rule.

         $\frac{5}{sin85}=\frac{a}{sin58.29}\\\\a=4.27$

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

Answer 2

The answer is c.           

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