Question:
Solution:
The diagram of a triangle ABC, where C is the right angle is:
Now, by definition and according to the data of the problem, we get that:
[tex]\cos (A)=\frac{5}{8}=\frac{adjacent\text{ side to the angle A}}{hypotenuse}[/tex]
that is:
now, to find the cos(B), first, we must find the missing side of the triangle. To do that, we can apply the Pythagorean theorem:
[tex]BC\text{ =}\sqrt[]{8^2-5^2}\text{ = }\sqrt[]{39}[/tex]
now, with respect to angle B, we obtain that:
[tex]\cos (B)=\frac{adjacent\text{ side to the angle B}}{hypotenuse}=\frac{\sqrt[]{39}}{8}[/tex]
So that, we can conclude that the correct answer is:
[tex]\frac{\sqrt[]{39}}{8}[/tex]
