MATH SOLVE

3 months ago

Q:
# What is the measure of ∠W, rounded to the nearest degree? 19° 32° 56° 71°

Accepted Solution

A:

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 = βSince the internal angles of a triangle add up to 180 degrees, then:α + α + β = 1802α + β = 180β = 180 - 2αUsing 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°