For an acute angle measuring x^, (x^) = 0.42. What is the value of ((90 - x)^)?

SAT Right triangles and trigonometry Practice Question 14 (Medium)

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Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

For an acute angle measuring $x^\circ$ , $\sin(x^\circ) = 0.42$ . What is the value of $\cos((90 - x)^\circ)$ ?

$0.58$

$0.42$

$0.91$

$2.38$

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Answer: B

The sine of an acute angle equals the cosine of its complement. Since $x^\circ$ and $(90 - x)^\circ$ are complementary, $\cos((90 - x)^\circ) = \sin(x^\circ) = 0.42$ .

Choice A is $1 - 0.42$ , but sine and cosine of complementary angles are equal, not values that add to $1$ .

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