# 30-60-right triangle properties

Discussion in 'Recreational Math' started by Greg Neill, Oct 15, 2008.

1. ### Greg NeillGuest

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.

Greg Neill, Oct 15, 2008

2. ### donGuest

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

don, Oct 15, 2008

3. ### donGuest

don, Oct 16, 2008
4. ### Greg NeillGuest

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.

Greg Neill, Oct 16, 2008
5. ### donGuest

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......

don, Oct 16, 2008
6. ### Michael StemperGuest

Are you aware that the hypotenuse of a 30-60-90 triangle will *always*
be twice the length of the short leg?

Michael Stemper, Oct 17, 2008