Question

Pls help me not fail

Answer 1

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 = $\sqrt{356.2}$ ≈ 18.9

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Using the Sine rule to find ∠ A

$\frac{18}{sinA}$ = $\frac{18.9}{sin75}$ ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = $\frac{18sin75}{18.9}$ , then

∠ A = $sin^{-1}$ ( $\frac{18sin75}{18.9}$ ) ≈ 66.9°