Question

State whether the given measurements determine zero, one, or two triangles.

B = 81°, b = 26, c = 28

Answer 1

Let's apply the law of sine to calculate angle C
sin(81)/26 = sin(C)/28
0.1646 = sin(C)/28 and sin(C) =1.063. Sine sin(α) cannot be > than 1, so this triangle is invalid

Answer 2

Explanation:

Alright, lets get started.

Side b = 26

Side c = 28

Angle B = 81

Using sin law

`(sinB)/(b)=(sinC)/(c)`

`(sin81)/(26)=(sinC)/(28)`

`sinC= (28sin81)/(26)`

`sinC= (28*0.98769)/(26)=1.06`

We got sin C value 1.06 which is more than 1, that is not possible because its out of range for sin function.

It means triangle is not possible.

Hence Zero triangle. : Answer

Hpe it will help :)