Elementary Geometry for College Students (6th Edition)

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

Chapter 11 - Section 11.2 - The Cosine Ratio and Applications - Exercises - Page 503: 3

Answer

cos α = $\frac{3}{5}$, cos β = $\frac{4}{5}$

Work Step by Step

Step 1: By Pythagoras theorem $6^{2}$ + $a^{2}$ = $10^{2}$ $a^{2}$ = 100 - 36 a = $\sqrt 64$ = 8 a = 8 Step 2: cos α = $\frac{length of adjacent}{length of hypotenuse}$ cos α = $\frac{6}{10}$ = $\frac{3}{5}$ Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$ cos β = $\frac{a}{10}$ =$\frac{8}{10}$ = $\frac{4}{5}$ Therefore cos α = $\frac{3}{5}$, cos β = $\frac{4}{5}$
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