How High is the Building?
Date: 03/08/2002 at 18:35:08 From: Nancy Subject: Angle of elevation Melissa and her friends decide to fly their paper airplanes out of the window of a tall building (one that has windows that open). Delbert is part of the ground crew, and Janet is the launch director. Delbert sights the window at a 75-degree angle from the ground, then backs up 25 ft and sights it again, this time at a 64-degree angle. How high is the window? What is the formula for this problem and how do I work it out? Thanks for the help, Nancy
Date: 03/08/2002 at 19:15:06 From: Doctor Jeremiah Subject: Re: Angle of elevation Hi Nancy, The first time he looks there is a triangle that looks like: + |\ | \ | \ h \ | \ | 75\ +--x---+ And the second time there is a triangle that looks like: + |\ | \ | \ h \ | \ | 64\ +-x+25-+ If you solve the first triangle for x and use that when you solve the second triangle for h, it will be easy to answer. Try it, but write back if you get stuck. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
Date: 03/10/2002 at 21:43:09 From: Nancy Subject: Angle of elevation I still don't know what to do. I don't understand how to do the first part. I don't have the X and I don't know the formula or method to use. Thanks, Nancy
Date: 03/11/2002 at 01:25:33 From: Doctor Jeremiah Subject: Re: Angle of elevation(I don't know) Hi Nancy, Any time both angles and distances are used, trignometry is involved. There is a lot of stuff about trignometry in the Frequently Asked Questions area and in the archives that would probably help you out. Check out these pages: Trigonometry Formulas http://mathforum.org/dr.math/faq/formulas/faq.trig.html Basics of Trigonometry http://mathforum.org/dr.math/problems/coley.12.12.01.html So from the first triangle: + |\ | \ | \ h \ | \ | 75\ +--x---+ We can get that the tan(75) = h/x, which means x tan(75) = h And from the second triangle: + |\ | \ | \ h \ | \ | 64\ +-x+25-+ We can get that the tan(64) = h/(x+25), which means (x+25) tan(64) = h So we have these two equations: x tan(75) = h (x+25) tan(64) = h Now, since both those equations are equal to h they must be equal to each other: x tan(75) = (x+25) tan(64) x tan(75) = x tan(64) + 25 tan(64) x tan(75) - x tan(64) = 25 tan(64) x (tan(75) - tan(64)) = 25 tan(64) x = 25 tan(64) / (tan(75) - tan(64)) Which can be solved with a calculator. Then you take x tan(75) = h and stick in that value of x and solve for h. Write back if you are still confused. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.