In the figure above, in the measure of angle 1 is not equal to the measure of angle 4, then the cosine of which of the following is equal to the sine of angle 1?

A) angle 3 only
B) angle 4 only
C) angles 2 and 4 only
D) angles 3 and 4 only
E) angles 2, 3, and 4

I’ll post the figure in the comments. 🙂

Go ahead and post the figure in the comments, but for future reference, a nice thing about this new Q&A is that you can add a URL of the image when you ask, instead of having to wait. Try it out next time!

Comments (4)

Angles 1 and 3 are the same, and angles 2 and 4 are the same. You can see this more easily if you plug in. Say angle 1 is 20 degrees. then the other angle in that smallest right triangle must be 70 degrees. That means angle 4 is also 70 degrees because of vertical angles. It also means that angle 3 must be 20 degrees, because the BIGGEST right triangle must add up to 180. If angle 3 is 20 degrees, then angle 2 must be 70 degrees because of the medium-sized right triangle.

The sine of angle 1 will be the same as the cosine of angle 4. Because angle 4 is the same as angle 2, the sine of angle 1 will ALSO be the equal to the cosine of angle 2. The answer is C.

In any right triangle, you have two non-right angles–let’s call them A and B. Because of SOH-CAH-TOA, sin A = cos B, and cos A = sin B.

Because angle 4 is vertical to an angle in a right triangle that’s opposite angle 1, we can say the sine of angle 1 will be the same as the cosine of angle 4.

Does that help?

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