Is this statement always, sometimes, or never true?For two acute angles ∠J and ∠K, if m∠J+m∠K=90°, then sin(J)=cos(K).alwayssometimesneverSubmit
Question
Is this statement always, sometimes, or never true?For two acute angles ∠J and ∠K, if m∠J+m∠K=90°, then sin(J)=cos(K).alwayssometimesneverSubmit
Solution
The statement is always true. This is because in a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. This is a direct result of the definitions of sine and cosine. Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse, while cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In a right triangle, the side opposite one acute angle is the adjacent side for the other acute angle, so their sine and cosine are equal. Therefore, if ∠J and ∠K are acute angles in a right triangle and m∠J+m∠K=90°, then sin(J)=cos(K) is always true.
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