Question

In right triangle ABC, shown below, cos C 9√130/9 find AC.

Answer 1

AC = 9

Explanation:

`cosine=(adjacent)/(hypotenuse)\\\\\text{We have:}\\\\\cos C=(9√(130))/(130)\\\\adjacent=AC\\\\hypotenuse=√(130)\\\\\text{Substitute:}\\\\(9√(130))/(130)=(AC)/(√(130))\qquad\text{cross multiply}\\\\130AC=(9√(130))(√(130))\qquad\text{use}\ √(a)\cdot√(a)=a\\\\130AC=(9)(130)\qquad\text{divide both sides by 130}\\\\(130AC)/(130)=((9)(130))/(130)\\\\AC=9`