Question 537190: If a=x and c=2x, how am I able to determine the Sine, Cosine and Tangent without numeric values? How am I able to determine the value of x if that is the only information I'm given?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You may not need to find a value of x to find the sine, cosine and tangent, but you do need more information than what you wrote.
If a right triangle goes with those values, like this
 you have enough information.
If they just tell you that ABC is a triangle with a right angle at C, it is the same thing, and you have enough information.
If you do not know that it is a right triangle, then there is no way to solve the problem.
If you know it is a right triangle, but you do not know which angle is the right angle, then there could be more than one answer set, because c could be the hypotenuse, or it could be one of the legs of the right triangle.
I will assume it's a right triangle and side c=2x is the hypotenuse (as in my drawing).
The right angle, opposite the hypotenuse would be called C (with the same letter, but using capitals).
The angle opposed to side a is normally called A.
The other angle and its opposite side would be B and b respectively.
The trigonometric ratios are define as
sinA = opposite side/hypotenuse, so sinA = a/c
cosA = adjacent side/hypotenuse, so cosA = b/c, and
tanA = opposite side/adjacent side, so tanA = a/b
You know that sinA = a/c = x/2x = 1/2
If you'd already been taught that, you would know that means A =30 degrees or  ,
and you would know the values for cosine and tangent of that angle.
Otherwise, you would have to calculate the length of side b using Pythagoras theorem to continue.
 -->  -->  -->
Then cosA =  and
tanA =
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