Which Side is Longer?
Date: 27 Jan 1995 12:00:21 -0500 From: Janice Cohrs Subject: geometry The following problem appeared on an assignment and I am having trouble justifying the answer key's solution. You are given a quadrilateral, ABCD, with diagonal DB, angle ADC = 90, angle DBC = 43, angle C = 91, side AD = 9, side DC = 9. Find which is longer AB or AD. Please send me a solution with explanation at firstname.lastname@example.org Thank you!
Date: 28 Jan 1995 11:51:21 -0500 From: Elizabeth Weber Subject: Re: geometry Hello Janice! Draw a picture of what you've described. You are given a quadrilateral, ABCD, with diagonal DB, angle ADC = 90, angle DBC = 43, angle C = 91, side AD = 9, side DC = 9. You know the measures of angle DBC and angle C. Since the sum of the angles of a triangle must add to 180, you know that angle BDC must be 46. This will let you use the rule of sines to find the length of side BC; which comes to about 9.5. Now, parts of your drawing will look like this: A |B | | | |9.5 9| | | | |__________| D 9 C Even if angle C measured 90 degrees, side AB would have to be longer than 9, because it would have to go a horizontal distance of 9, and an additional vertical distance of 0.5. Since angle C measures 91, degrees, corner B is even further from corner A, making side AB all the longer. Side AB must be longer than 9; it must be longer than side AD. -Elizabeth, a math doctor
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