Answer:
All possible values of ∠Y are 76.6° and 103.4°
Step-by-step explanation:
In Δ WXY
∵ x is the opposite side of ∠X
∵ y is the opposite side of ∠Y
→ By using the sine rule
∴ [tex]\frac{x}{sin(X)}[/tex] = [tex]\frac{y}{sin(Y)}[/tex]
∵ x = 85 and y = 88
∴ m∠X = 70°
→ Substitute them in the rule above
∴ [tex]\frac{85}{sin(70)}[/tex] = [tex]\frac{88}{sin(Y)}[/tex]
→ By using the cross multiplication
∴ 85 × sin(Y) = 88 × sin(70)
→ Divide both sides by 85
∴ sin(Y) = 0.9728582427
∴ m∠Y = [tex]sin^{-1}[/tex](0.9728582427)
∴ m∠Y = 76.62037845
→ Round it to the nearest tenth
∴ m∠Y = 76.6°
→ The other value of ∠Y is the obtuse angle supplement of ∠Y
∴ m∠Y = 180 - 76.6
∴ m∠Y = 103.4°
∴ All possible values of ∠Y are 76.6° and 103.4°
