Help with geometry problem

timer Asked: Nov 3rd, 2015
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Question Description

Tutor Answer

Samuel H.
School: New York University

Thank you for the opportunity to help you with your question!

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  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

Please let me know if you need any clarification. I'm always happy to answer your questions.

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awesome work thanks

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