Question

Pls help me not fail

Answer 1

D

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 =
`√(356.2)` ≈ 18.9

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Using the Sine rule to find ∠ A

`(18)/(sinA)` =
`(18.9)/(sin75)` ( cross- multiply )

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

sinA =
`(18sin75)/(18.9)` , then

∠ A =
`sin^(-1)` (
`(18sin75)/(18.9)` ) ≈ 66.9°