Answer:
71°
Step-by-step explanation:
This is an isosceles triangle because it has two sides with lengths, hence the angles opposite the equal sides are also equal, that is ∠U = ∠V.
So we can say that:
∠U = ∠V = α
∠W = β
Since the internal angles of a triangle add up to 180 degrees, then:
α + α + β = 180
2α + β = 180
β = 180 - 2α
Using the law of sine:
[tex]\frac{35}{sin\beta} =\frac{30}{sin\alpha} \\ \\ \frac{35}{sin(180 - 2\alpha)} =\frac{30}{sin\alpha} \\ \\ \\ From \ Properties: \\ \\ sin(180-2\alpha)=sin(180)cos2\alpha-sin2\alpha cos(180) \\ \\ = -sin2\alpha(-1)=sin2\alpha \\ \\ Also: \\ \\ sin2\alpha=2sin\alpha cos\alpha[/tex]
Therefore:
[tex]\frac{35}{2sin\alpha cos\alpha} =\frac{30}{sin\alpha} \\ \\ \therefore \frac{35}{60}=cos\alpha \\ \\ \alpha=cos^{-1}(\frac{7}{12})=54.31^{\circ}[/tex]
But we want to know ∠W = β, therefore:
[tex]\beta = 180 - 2\alpha \\ \\ \beta =180-2(54.31)=71.37^{\circ}[/tex]
And rounded to the nearest degree:
∠W = 71°
