# Chapter 5 - Test - Page 250: 8b

$cos(A+B) = -\frac{56}{65}$

#### Work Step by Step

If the hypotenuse is 13, and the opposite side is 5, then the length of the adjacent side is $\sqrt{13^2-5^2} = 12$ If the hypotenuse is 5, and the adjacent side is 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$ $cos(A+B) = cos~A~cos~B-sin~A~sin~B$ $cos(A+B) = (\frac{12}{13})(-\frac{3}{5})-(\frac{5}{13})(\frac{4}{5})$ $cos(A+B) = -\frac{36}{65}-\frac{20}{65}$ $cos(A+B) = -\frac{56}{65}$

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