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#