Answer:
D
Step-by-step explanation:
Using the Cosine rule to find AC
AC² = BC² + AB² - (2 × BC × AB × cosB )
= 18² + 12² - ( 2 × 18 × 12 × cos75° )
= 324 + 144 - 432cos75°
= 468 - 111.8
= 356.2 ( take the square root of both sides )
AC = [tex]\sqrt{356.2}[/tex] ≈ 18.9
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Using the Sine rule to find ∠ A
[tex]\frac{18}{sinA}[/tex] = [tex]\frac{18.9}{sin75}[/tex] ( cross- multiply )
18.9 sinA = 18 sin75° ( divide both sides by 18.9 )
sinA = [tex]\frac{18sin75}{18.9}[/tex] , then
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{18sin75}{18.9}[/tex] ) ≈ 66.9°
