Is this statement always, sometimes, or never true?If ∠Y and ∠Z are acute angles in an isosceles right triangle, then cos(Y)=cos(Z).
Question
Is this statement always, sometimes, or never true?If ∠Y and ∠Z are acute angles in an isosceles right triangle, then cos(Y)=cos(Z).
Solution
The statement is sometimes true. In an isosceles right triangle, the two acute angles are not always equal. One angle is always 45 degrees, while the other is 90 degrees minus the first angle. Therefore, the cosine of the two angles will be equal only when the two angles are equal, which is when they are both 45 degrees. In all other cases, the cosine of the two angles will not be equal.
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