Answer:
≈ 94.9 mi²
Step-by-step explanation:
The area (A) of Δ WXY can be calculated as
A = [tex]\frac{1}{2}[/tex] × WY × WX × sinW
∠ W = 180° - (40 + 21)° = 180° - 61° = 119°
Calculate WX using the Sine rule, that is
[tex]\frac{11}{sin21}[/tex] = [tex]\frac{WX}{sin40}[/tex] ( cross- multiply )
WX sin21° = 11 sin40° ( divide both sides by sin21° )
WX = [tex]\frac{11sin40}{sin21}[/tex] ≈ 19.73 mi , thus
A = 0.5 × 11 × 19.73 × sin119° ≈ 49.9 mi² ( to the nearest tenth )
