Chapter 11.3, Problem 8MRE

To determine

To Complete: In triangle $ABC$ if $m\angle C=90,AC=8,AB=17$ then $\cos B=\mathrm{...}$

Answer to Problem 8MRE

  $\cos B=\frac{15}{17}$

Explanation of Solution

Given: In triangle $ABC$ if $m\angle C=90,AC=8,AB=17$ then $\cos B=\mathrm{...}$ .

  

Using Pythagoras theorem to find base of the triangle.

  $\begin{array}{l}{17}^2=8^2+b^2\\ b^2={17}^2-8^2\\ b^2=289-64\\ b^2=225\\ b=15\\ \end{array}$

Now

  $\begin{array}{l}\cos B=\frac{CB}{AB}\\ \cos B=\frac{15}{17}\end{array}$

Hence, $\cos B=\frac{15}{17}$