Question

Select the true statement about triangle ABC.

A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C

Answer 1

B

Explanation:

We know that cosθ= adjacent/hypotenuse, sinθ=opposite/hypotenuse, and tanθ=opposite/adjacent.

Using this, we can first try between cos and sin for A-C. We know that two different angles will not have the same side adjacent to both of them. However, one angle might have an adjacent side that is opposite to another angle. Using this knowledge, we can say that A is incorrect, as two different angles in the same triangle cannot have the same cos value (unless the triangle is isosceles).

For B, we can say that cos A = adjacent/hypotenuse = 12/13, and sin C= opposite/hypotenuse = 12/13. These are equal, but we can double check by making sure the other answers are wrong.

For C, we can tell that B is a right angle, signified by the small square representing the angle. sin(90°) = 1, and cosA = 12/13. These are not equal.

Finally, for D, sin A = opposite/hypotenuse = 5/13, while tan C = opposite/adjacent = 12/5. These are not equal