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Here we are going to need to use one of the three trigonometric identities:

sin(x) = opposite / hypotenuse, cos(x) = adjacent / hypotenuse, tan(x) = opposite / adjacent

We are given the length of the hypotenuse (the longest side) and the angle x and we are asked to find the length of the opposite side.

Therefore we will use the equation sin(x) = opposite / hypotenuse.

To find the value of the opposite side, we can rearrange this equation to leave opposite by itself on one side of the equals sign:

sin(x) * hypotenuse = opposite

Substituting our values for x and the hypotenuse we get:

opposite = sin(47) * 51

Using a calculator this gives:

opposite = 37.3

and so the answer is a = 37.3

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