X=37 degrees, y=75 degrees, a=6. Using the law of sines, how do you solve the triangle, finding all parts of the triangle?

1 Answer
May 19, 2018

alpha = 37^∘
beta = 75^∘
gamma = 68^∘

a= 6
b ≈9.63
c≈9.244

Explanation:

law of sines:

sin(alpha)/a=sin(beta)/b=sin(gamma)/c

let alpha = 37^∘

let beta = 75^∘

gamma = 180^∘ - 37^∘ - 75^∘ = 68 ^∘
(total of a triangle is 180^∘)

Given: a=6

sin(37^∘)/6=sin(75^∘)/b

bsin(37^∘)=6sin(75^∘)

b=(6sin(75^∘))/sin(37^∘) ≈ 9.63

Now to find side c:

sin(37^∘)/6=sin(68^∘)/c

csin(37^∘)=6sin(68^∘)

c=(6sin(68^∘))/sin(37^∘) ≈ 9.244