Question

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

Answer 1

the answer is c.

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Answer 2

Number of distinct triangles = 1

Explanation:

We have sine rule
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`.

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

Substituting

`(5)/(sin85)=(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.

`(5)/(sin85)=(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