Answer:
The length of w is 0.8 cm
Step-by-step explanation:
In Δ WXY
x is the opposite side to ∠X
w is the opposite side to ∠W
y is the opposite side to ∠Y
∵ m∠X = 45°
∵ m∠Y = 108
∵ The sum of the measures of the interior angle of a triangle is 180°
∴ 45 + 108 + m∠W = 180
→ Add the like terms in the left side
∵ 153 + m∠W = 180
→ Subtract 153 from both sides
∴ m∠W = 27°
Now we can use the sine rule to find the length of w
∵ [tex]\frac{w}{sin(W)}[/tex] = [tex]\frac{x}{sin(X)}[/tex] = [tex]\frac{y}{sin(Y)}[/tex]
→ Use the first 2 ratios to find w
∵ x = 1.2 cm
∵ [tex]\frac{w}{sin(27)}[/tex] = [tex]\frac{1.2}{sin(45)}[/tex]
→ By using cross multiplication
∴ w × sin(45) = 1.2 × sin(27)
∴ w sin(45) = 1.2 sin(27)
→ Divide both sides by sin(45)
∴ w = 0.7704474263
→ Round it to the nearest tenth
∴ w = 0.8 cm
∴ The length of w is 0.8 cm
