Answer:
b= 27.46
A= 61 degree
C= 83 degree
Step-by-step explanation:
Solve the triangle. B=36 a=41 c=20
Apply cosine rule to find the side length B
[tex]b^2= a^2 +c^2-2acsin(A)[/tex]
[tex]b^2 = 41^2 + 20^2 - 2 \cdot 20 \cdot 41 \cdot cos 36[/tex]
Take square root on both sides
so b=27.46292
b= 27.46
Now use sine rule to find the angles A and C
[tex]\frac{Sin A}{a} = \frac{Sin B}{b}[/tex]
[tex]\frac{Sin A}{41} = \frac{Sin 36}{27.46}[/tex]
Cross multiply it
[tex]27.46 sin(A)= 41 sin(36)[/tex]
[tex]Sin(A) = \frac{41 Sin 36}{27.46}[/tex]
A= [tex]sin^{-1}(\frac{41 Sin 36}{27.46})[/tex]
A= 61 degree
Angle A + angle B + angle C= 180
[tex]61+36 + angle C= 180[/tex]
Angle C= 83 degree
