Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 11 - Section 11.2 - The Cosine Ratio and Applications - Exercises - Page 511: 5

Answer

cos α = $\frac{sqrt of 2}{sqrt of 3}$ , cos β = $\frac{sqrt of 3}{sqrt of 5}$

Work Step by Step

Step 1: By Pythagoras theorem $(sqrt of 3)^{2}$ + $(sqrt of 2)^{2}$ = $c^{2}$ 3 + 2 = $c^{2}$ c = $\sqrt 5$ Step 2: cos α = $\frac{length of adjacent}{length of hypotenuse}$ cos α = $\frac{sqrt of 2}{sqrt of 3}$ Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$ cos β = $\frac{sqrt of 3}{sqrt of 5}$ Therefore cos α = $\frac{sqrt of 2}{sqrt of 3}$ , cos β = $\frac{sqrt of 3}{sqrt of 5}$
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