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