SOLUTION: Can someone prove to me why tan (47.3 degrees) = 13/15? When I draw a right triangle and label the sides, I do not get tan = 13/15. Is this because we don't have a right triangle

Question 1063506: Can someone prove to me why tan (47.3 degrees) = 13/15? When I draw a right triangle and label the sides, I do not get tan = 13/15. Is this because we don't have a right triangle here?
For a right triangle, hypotenuse is 13, the longer arm is 12, and shortest side is 5. The remaining two angles are 45 degrees each. So, tan (45 degrees) in right triangle = opp/adj = sin/cos = 12/5 (assuming I drew the longer side across from 45 degree angle).
I guess this is why my standard set up for 45 degree angle in 45-45-90 triangle did not come out, because we don't have this triangle. (One of the angles in my triangle is 47.3 degrees).
Here is the question I was trying to answer:
arctan(13/12)=47.3 degrees.
Which of the following is true?
I said:
theta=47.3 degrees, therefore, tan(47.3 degrees)=13/12.
So, if we take tan of 47.3 degrees, we get 13/12=1.08.
Found 2 solutions by sky1983, ikleyn:
Answer by sky1983(10) (Show Source): You can put this solution on YOUR website!
If you want to prove that tan 47.3 = 13/15, draw a right angle, one side measuring 13 and the other measuring 15 then connect the end points of the two sides to form the hypotenuse. Label your drawing. Remember that tan 47.3 is opposite side divided by adjacent side. Then use a protractor to measure the angle if it is 47.3. I did it. tan 47.3 is not equal to 13/15.
Right Triangle 5-12-13 has no 45 degree angle.
Using of a 45-45-90 is not accurate, better if you have a protractor.
Yes it is true that tan 47.3 = 13/12.
cheers mate!
sky1983
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
arctan(13/15) = 40.9 degrees.

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