Question

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?

Answer 1

`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`