Question

In triangle ABC below, (which is not drawn to scale, do not trust the picture, the following is true about the given trigonometric raitos.

sin(x) = cos(y)

what must be the measure of angle ABC, explain.

Answer 1

Since sin(x) = cos(y), we can write this as sin(x) = sin(90° - y), using the identity that cos(y) = sin(90° - y).

This means that angle x and angle (90° - y) have the same sine ratio, which implies that they must be equal or supplementary.

If angle x and angle (90° - y) are equal, then x = 90° - y, and angle BAC would be (x + y) = (90° - y + y) = 90°.

If angle x and angle (90° - y) are supplementary, then x + (90° - y) = 180°, which implies that angle BAC is equal to (x + y) = [(180° - (90° - y)) + y] = 90° + y.

Therefore, the measure of angle ABC cannot be determined uniquely based on the given information.