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a boat on a river has a 27 degree angle of elevation to the top of a dam and the dam is 1037ft from the river.How far is the boat from the base of the dam.

is the answer sin27 degrees = 1037/x.
=x =1037/sin27 degrees?

No, the sine involves the hypotenuse. You are working with the legs of the triangle.
If you wanted the distance to the top of the dam, then you would be right.

However,

1037/x = tan27
so,
x = 1037/tan27

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