Is this statement always, sometimes, or never true?If ∠X and ∠Y are acute angles in a scalene right triangle, then cos(X)=sin(Y).alwayssometimesneverSubmit
Question
Is this statement always, sometimes, or never true?If ∠X and ∠Y are acute angles in a scalene right triangle, then cos(X)=sin(Y).alwayssometimesneverSubmit
Solution
The statement is always true. In a right triangle, the acute angles are complementary, meaning they add up to 90 degrees. The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse, while the sine of an angle is defined as the ratio of the opposite side to the hypotenuse. Because the angles are complementary, the side that is "adjacent" to one angle is "opposite" to the other, and vice versa. Therefore, the cosine of one acute angle will always equal the sine of the other.
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