Question

Solve the triangle. B=36 a=41 c=20

Answer 1

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

$b^2= a^2 +c^2-2acsin(A)$

$b^2 = 41^2 + 20^2 - 2 \cdot 20 \cdot 41 \cdot cos 36$

Take square root on both sides

so b=27.46292

b= 27.46

Now use sine rule to find the angles A  and C

$\frac{Sin A}{a} = \frac{Sin B}{b}$

$\frac{Sin A}{41} = \frac{Sin 36}{27.46}$

Cross multiply it

$27.46 sin(A)= 41 sin(36)$

$Sin(A) = \frac{41 Sin 36}{27.46}$

A= $sin^{-1}(\frac{41 Sin 36}{27.46})$

A= 61 degree

Angle A + angle B + angle C= 180

$61+36 + angle C= 180$

Angle C= 83 degree

Answer 2

Use cosine rule:-
b^2 = 41^2 + 20^2 - 2*20*41*cos 36

       =   754.21

b =  27.5 

you can now find angle A using the sine rule

27.5 / sin 36  = 41 / sin A

sin A  =   0.87633

< A =  61.2 degrees