SOLUTION: I have a right angle triangle with 2 given sides. adjacent = 3 and the opposite = 5. I need to find a solution for the six trigonometric functions. The system is not accepting my s

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Question 1155306: I have a right angle triangle with 2 given sides. adjacent = 3 and the opposite = 5. I need to find a solution for the six trigonometric functions. The system is not accepting my solution of 5.8 for the hypotenuse, so I was wondering what I may have miscalculated.
Thanks
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
I have a right angle triangle with 2 given sides. adjacent = 3 and the opposite = 5. I need to find a solution for the six trigonometric functions. The system is not accepting my solution of 5.8 for the hypotenuse, so I was wondering what I may have miscalculated.
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Hypotenuse = sqrt(3^2 + 5^2) = sqrt(34) =~ 5.831
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Maybe it's a matter of # of digits?
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a = short side = 3
b = 5
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A = angle opposite a, B opposite b
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6 functions of which angle?
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r = sqrt(34)
sin(A) = 3/r
cos(A) = 5/r
tan(A) = 3/5
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cot = 1/tan
sec = 1/cos
csc = 1/sin
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Adj = 3 and Opp = 5 is angle B.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
adjacent = 3
opposite = 5
hypotenuse is sqrt(3^2 + 5^2) = sqrt(9 + 25) = sqrt(34) = 5.830952895.
round that off to 1 decimal point and you get 5.8.
that's only approximate though.
the exact answer is sqrt(34)
that does not appear to be simplified any further than that.

unless they asked for the answer to the nearest tenth, then 5.8 probably won't do it.
your solution for the 6 trigonometric functions should be:

sine = opposite / hypotenuse = 5 / sqrt(34)

cosine = adjacent / hypotenuse = 3 / sqrt(34)

tangent = opposite / adjacent = 5 / 3

cotangent = adjacent / opposite = 3 / 5

secant = hypotenuse / adjacent = sqrt(34) / 3

cosecant = hypotenuse / opposite = sqrt(34) / 5

note that sine = 5 / sqrt(34) can be simplified to (5 * sqrt(34) / 34.

not that cosine = 3 / sqrt(34) can be simplified to (3 * sqrt(34) / 34

note that secant = 1 / cosine = 1 / (3 / sqrt(34)) = 1 * sqrt(34) / 3 = sqrt(34) / 3

note that cosecant = 1 / sine = 1 / (5 / sqrt(34)) = 1 * sqrt(34) / 5 = sqrt(34) / 5

note that cotangent = 1 / tangent = 1 / (5/3) = 1 * 3/5 = 3/5

mpte that tangent also equals sine / cosine = (5 / sqrt(34) / (3 / sqrt(34)) =
5 / sqrt(34) * sqrt(34) / 3 = 5 / 3

the answer to your questions should be:\

hypotenuse = sqrt(34)

sine = 5 / sqrt(34) = 5 * sqrt(34) / 34

cosine = 3 / sqrt(34) = 3 * sqrt(34) / 34

tangent = 3/5

cotangent = 5/3

secant = sqrt(34) / 3

cosecant = sqrt(34) / 5