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

sides are a = 16 c = 14 b =22.96

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

Explanation:

using sine law of triangle,

`(sin A)/(a) = (Sin B)/(b)= (sinC)/(c)`

using,

`(sin A)/(a) = (sinC)/(c)`

given that,

C= 37° a = 16 c = 14

now,

`(sin A)/(16) = (sin37^o)/(14)`

sin A = 0.687

A = 43.39°

hence B = 180° - (43.39° + 37°)

B = 99.61°

`(sin 43.39^o)/(16) = (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°