If sin x degree = cos 56 degree, find x. Solve by using right-angled triangles. 

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bridgetrbcs eNotes educator| Certified Educator


First, I would draw a right triangle so that I could label the parts.  Mark your 90 degree angle, and make one of the other two angles 56 degrees.  Remember that a triangle is made of three angles whose sum (adding up) is 180 degrees.  We have used 146 of those 180 degrees in our triangle.

180-146=34  Label the last angle 34 degrees.

With your pencil on the 56 degree angle, find the adjacent side and the hypotenuse as these make cosine.  These two sides are also used in the 34 degree angle.  Put your pencil on the 34 degree angle and see what those same two sides would be.  They would be opposite and hypotenuse. Sine uses opposite and hypotenuse.  Therefore, cos 56 degrees is sin 34 degrees. 

If you have any other questions please feel free to ask and as always I hope this answer helps you in your studies!

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