Question

Determine the number of possible triangles, ABC, that can be formed given angle A = 30°, a = 4, and b = 6.

Answer 1

Answer:

Step-by-step explanation:

Alright, lets get started.

using Sine Law,

$\frac{sinA}{a}=\frac{sinB}{b}$

$\frac{sin30}{4}=\frac{sinB}{6}$

$sinB=0.75$

$angle B = 48.6$

Another angle will be

$angle B' = 180-48.6 = 131.4$

considering angle B, angle C = $180 - (48.6+30)=101.4$

considering angle B', angle C' = $180-(131.4+30)=18.6$

$\frac{sinA}{a}=\frac{sinC}{c}$

$\frac{sin30}{4}=\frac{sin101.4}{c}$

$c = 7.84$

Similarly, finding c'

$\frac{sinA}{a}=\frac{sinC'}{c'}$

$\frac{sin30}{4}=\frac{sin18.6}{c'}$

$c'=2.55$

Hence two triangles are possible with below details:  :   Answer

A = 30, B = 48.6, C = 101.4, c = 7.84

A = 30, B' = 131.4, C' = 18.6, c' = 2.55

Hope it will help :)