Is this sine, cosine, or tangent?

Question

There’s this right triangle that has a 90 degree angle. I don’t know what the opposite is because it’s opposite is the hypothenuse and there is no hypothenuse on the problem.

Answer 1

I think that you are trying to evaluate trig function values for angles that are multiples of 90°.  In such a case, "SOHCAHTOA" doesn't work.  

 

What we can do is use the unit circle definition of sine and cosine.  For example, if the angle is 90°, the point at the "top" of the circle, namely (0,1), is the same as (cos90°, sin90).

 

   So, cos90° = 0 and sin90° = 1

 

       Then, tan90° = (sin90°) / (cos90°) . So, tan90° is undefined

 

If the angle is 180°, then the leftmost point on the unit circle, (-1,0), is the same as (cos180°, sin180°).

 

    So, cos180° = -1 and sin180° = 0

 

       Then, tan180° = 0/(-1) = 0.

 

Answer 2

you are talking about a right triangle.  For purposes of discussion, let's say that angle C is 90 degrees, and we call the  side across from C "hypotenuse c"--this side is the longest side of the triangle. 

 

The other sides are called LEGS in a right triangle.

 

Choose either of the acute angles. OPPOSITE (across from) angle A is side a; across from angle B is side b; both of these are legs.

 

For angle A, sine is opposite side divided by hypotenuse; this would be a/c;

for angle A, cosine is adjacent side divided by hypotenuse; this would be b/c.

 

sin B = a/c; cos A = b/c.

 

You see, the term "opposite" has a different outcome depending on whether you are talking about acute angle A or B