Question

If COS(W) = sin(zº), which of the following statements is true?

Answer 1

Answer:

The third option is the answer.

Step-by-step explanation:

These triangles are clearly not congruent because they have different side length so the first 2 options are wrong.

Since both triangles already share a right angle. The other two angles in both triangles must both add up to 90.

It is given to use that sin z=cos w. That doesn't mean that angle z= angle w.

Consider a two similar two 30-60-90 triangles We are given the 90 degree right angle in both triangles. We are also given one 60 degree angle in one and a 30 degree triangle in one.

$\cos(30) = \sin(60)$

But they have two different angle measures.

However, by triangle interior theorem. The third angle must be

equal to the other corresponding angle of the other triangle. So angle z corresponds with Angle X.

By the AA theorem, The triangles are similar.

The third option is the answer.