# Chapter 11 - Section 11.2 - The Cosine Ratio and Applications - Exercises - Page 511: 4

cos α = $\frac{5}{3sqrt5}$, cos β = $\frac{2}{3}$

#### Work Step by Step

Step 1: By Pythagoras theorem $(sqrt of 5)^{2}$ + $a^{2}$ = $3^{2}$ $a^{2}$ = 9 - 5 a = $\sqrt 4$ = 2 a = 2 Step 2: cos α = $\frac{length of adjacent}{length of hypotenuse}$ cos α = $\frac{sqrt 5}{3}$ * $\frac{sqrt 5}{sqrt 5}$ = $\frac{5}{3sqrt5}$ Similarly cos β = $\frac{length of adjacent}{length of hypotenuse}$ cos β = $\frac{2}{3}$ Therefore cos α = $\frac{5}{3sqrt5}$, cos β = $\frac{2}{3}$

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