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Math Forum / Mathematics / Recreational Math / October 200830-60-right triangle properties
Given a 30-60-right triangle with the short leg equal to x and the hypotenuse = 2x ...... the question is find the cosine of angles alpha and beta? I'm using a book that never gives any answers :-( Trigonometry by I.M. Gelfand > Given a 30-60-right triangle with the short leg equal to x and the > hypotenuse = 2x ...... the question is find the cosine of angles alpha and > beta? > > I'm using a book that never gives any answers :-( Trigonometry by I.M. > Gelfand You say that it's a 30-60-right triangle? Then the angles are specified as 30, 60, and 90 degrees. So where do alpha and beta enter the picture? Anyways, draw a picture, fill in what you know. Invoke Pythagorus to find the missing data. Then read off your cosines as the appropriate ratios. > So where do alpha and beta > enter the picture? Well, according to the standard alpha represents the first angle in a right triangle and beta represents the second. http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics >> So where do alpha and beta >> enter the picture? [quoted text clipped - 3 lines] > > http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics A labelling convention need not always be applied. You simply have to be specific and consistent in your choices for a given problem. To avoid confusion, always spell out your definitions up front for any given problem. Did you solve your problem? > Did you solve your problem? Since the Hypotenuse is 2x and the short leg was x, the sine of alpha would be .5 indicating a 30 degree angle, leaving the other angle to be 60, so yes I guess I solved the problem if my thinking is correct... this damn book never gives an answer...... >Given a 30-60-right triangle with the short leg equal to x and the >hypotenuse = 2x ...... Are you aware that the hypotenuse of a 30-60-90 triangle will *always* be twice the length of the short leg?  SignatureMichael F. Stemper #include <Standard_Disclaimer> The name of the story is "A Sound of Thunder". It was written by Ray Bradbury. You're welcome. |
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