Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Review Exercises - Page 96: 58


$h=k(\tan B-\tan A)$

Work Step by Step

Name $x$ = the leg opposite to the angle $A$. Using TOA in SOHCAHTOA to find x, in the triangle where x is opposite to A: $\displaystyle \tan A=\frac{x}{k}$ $ x=k\tan A$ in the triangle where (x+h) is opposite to B: $\displaystyle \tan B=\frac{h+x}{k}$ $k\tan B=h+x$ $x=k\tan B-h$ Equate the two expressions for x and solve for h: $k\tan A=k\tan B-h$ $h=k\tan B-k\tan A$ $h=k(\tan B-\tan A)$
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