Question

In ΔABC , angle C is a right angle.

Answer 1

Answer:  Choice A. sin(A) = cos(B)

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Explanation:

The rule is that sin(A) = cos(B) if and only if A+B = 90.

Note how

• sin(A) = opposite/hypotenuse = BC/AB
• cos(B) = adjacent/hypotenuse = BC/AB

Since both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).

In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.

The side lengths can be anything you want, as long as you're dealing with a right triangle.