Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 65

Answer

x = 6.667$^{\circ}$ or = 6$\frac{2}{3}$$^{\circ}$ Thus, $\frac{450}{x}$ = 67.5$^{\circ}$ and, $\frac{150}{x}$ = 22.5$^{\circ}$

Work Step by Step

Given, that $\frac{450}{x}$ and $\frac{150}{x}$ are complementary angles. Thus, $\frac{450}{x}$ + $\frac{150}{x}$ = 90$^{\circ}$ Since denominators are same (x), thus we can directly add the numerators ( 450 and 150) Thus, $\frac{450}{x}$ + $\frac{150}{x}$ = $\frac{600}{x}$ Given $\frac{600}{x}$ = 90$^{\circ}$ , Thus x = $\frac{600}{90}$$^{\circ}$ = $\frac{20}{3}$$^{\circ}$ = 6.667$^{\circ}$ or = 6$\frac{2}{3}$$^{\circ}$ Thus $\frac{450}{x}$ = 450 $\div$ $\frac{20}{3}$ = 450 $\times$ $\frac{3}{20}$ = 67.5$^{\circ}$ $\frac{150}{x}$ = 150 $\div$ $\frac{20}{3}$ = 150 $\times$ $\frac{3}{20}$ = 22.5$^{\circ}$
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