Question

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

B = 86°, b = 21, c = 18

Answer 1

Now using rule of sines for a triangle I write\[\frac{ Sin B }{ b } = \frac{ SinC }{ c }\]

Answer 2

\[\frac{ Sin 86 }{ 21 } = \frac{ SinC }{ 18 }\]\[\frac{ .9976 }{ 21 } = \frac{ Sin C }{ 18 }\]

Solving this would give you

\[Sin C = .885\]

\[Angle \space C = 58.77° \]

Now sum of angles in a Triangle is 180°.

So Angle A = 180-86-58.77 = 35.23

So you can find the third side.

This will make only one Triangle

Answer 3

Alright. I'll remember this. Thank you.