Length of the Diagonals of a Parallelogram
Date: 05/22/2000 at 19:46:31 From: moose Subject: Calculus A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?
Date: 05/23/2000 at 11:53:07 From: Doctor Douglas Subject: Re: Calculus Hi Moose, This is more of a trigonometry/geometry problem than a calculus problem. First we draw a parallelogram: 10 A --------------- P(x,y) / / 6 / / 6 /_70deg________/ 10 B Now, what is the length of say, the long diagonal? If we superimpose a Cartesian xy grid on this with the origin at the lower left, we then need to find the coordinates of the point P(x,y) at the upper right. We use trigonometry (see lower left angle, left side) to compute these coordinates: x = (bottom of triangle at left) + (upper edge) = (6 cos(70 deg)) + (10) y = (height of triangle at left) = (6 sin(70 deg)) So the long diagonal is sqrt(x^2 + y^2), by the Pythagorean theorem. See if you can use similar reasoning to obtain the coordinates of points A and B to find the length of the short diagonal. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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