Answer:
The answer to your question is Perimeter = 287.3 in
Step-by-step explanation:
AB = 90 in
BC = 80 in
∠B = 50
Perimeter = ?
Process
1.- We need to find AC using Law of sines
[tex]\frac{sin A}{80} = \frac{sin 50}{90}[/tex]
[tex]sin A = \frac{80}{90} sin 50[/tex]
[tex]sin A = 0.68[/tex]
A = 42.9 ≈ 43
The sum of the internal angles in a triangle equals 180°
A + B + C = 180°
43 + B + 50 = 180
B = 180 - 43 - 50
B = 87°
[tex]\frac{AC}{Sin 87} = \frac{90}{sin 50}[/tex]
[tex]AC = 90 \frac{sin 87}{sin 50}[/tex]
AC = 117.3
2.- Find the perimeter
Perimeter = AB + BC + AC
Perimeter = 90 + 80 + 117.3
Perimeter = 287.3 in
