Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 241: 31


By using the same process that we used in excercise 30 which is applying the pythagorean theorem in each small triangle then create a system of equation. We obtain two pythagorean equations : $ 10^{2} = ( y-26 )^{2}+ h^{2} $ $ 24^{2}=y^{2}+h^{2} $ Therefore $ y= \frac{120}{13} $ By substituting $y$ in one of the equation above Then the $ h= \frac{288}{13}\approx 9.2 $

Work Step by Step

I used the equation for altitude, as well as a rough sketch to keep track of the location of the triangle's values, to obtain my solution.
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