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

Number of distinct triangles = 1

Step-by-step explanation:

We have sine rule .

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

Substituting

We also have

          A+B+C = 180°

          A+85+36.71 = 180

          A = 58.29°

Substituting in sine rule.

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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction