Question

State whether the given measurements determine zero, one, or two triangles. C = 37°, a = 16, c = 14

Answer 1

Two triangles: b ≈ 2.62 or 22.94

Answer 2

Answer:

sides are     a = 16                   c = 14             b =22.96

angles are   A = 43.39°           B = 99.61°        C = 37°

Step-by-step explanation:

using sine law of triangle,

$\frac{sin A}{a} = \frac{Sin B}{b}= \frac{sinC}{c}$

using,

$\frac{sin A}{a} = \frac{sinC}{c}$

given that,

C= 37°                 a = 16                   c = 14

now,

$\frac{sin A}{16} = \frac{sin37^o}{14}$

sin A = 0.687

A = 43.39°

hence B = 180° - (43.39° + 37°)

           B = 99.61°

$\frac{sin 43.39^o}{16} = \frac{sin99.61^o}{b}$

b = 22.96

Hence, there will be only one triangle which will form and there

sides are     a = 16                   c = 14             b =22.96

angles are   A = 43.39°           B = 99.61°        C = 37°