SOLUTION: There is a right triangle (not to scale), the adjacent side is 11 inches, the hypotenuse is x (the value to be found), and the adjacent angle is 28 degrees. I have to use either si

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Question 623063: There is a right triangle (not to scale), the adjacent side is 11 inches, the hypotenuse is x (the value to be found), and the adjacent angle is 28 degrees. I have to use either sine, cosine, or tangent. The options are:
a.)12.5 in.
b.)10 in.
c.)13 in.
d.)9.7 in.
I used cosine and got 9.7, but on the online course I'm taking it said "d.)9.7 in." is not the correct answer. Could you please help me find the correct answer and explain how you did it? Thank you.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
Since the side you have is the adjacent side and the side you want is the hypotenuse, cos is the correct function to use. Apparently something wen wrong in how you used cos.

Think about this: The hypotenuse is always the longest side of a right triangle. So how could it be 9.7 when the adjacent side is 11? It can't. It has be longer than 11. We already know that the only possible answers are (a) or (c).

cos is adjacent over hypotenuse. So the equation you should start with is:

(I suspect that you had the ratio upside down.) To solve this we get rid of the fraction by multiplying each side by x:

Then we solve for x by dividing both sides by cos(28):

Now we reach for our calculator: