Answer:
[tex]cos\ V = \frac{2\sqrt{29}}{29}[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find cos V
In trigonometry:
[tex]cos\theta = \frac{Adjacent}{Hypotenuse}[/tex]
In this case:
[tex]cos V= \frac{TV}{UV}[/tex]
Where
[tex]TV = 6[/tex]
and
[tex]UV^2 = TV^2 + TU^2[/tex] -- Pythagoras
[tex]UV^2 = 6^2 + 15^2[/tex]
[tex]UV^2 = 261[/tex]
Take square roots
[tex]UV = \sqrt{261[/tex]
[tex]UV = \sqrt{9*29[/tex]
[tex]UV = \sqrt{9} *\sqrt{29[/tex]
[tex]UV = 3\sqrt{29[/tex]
So:
[tex]cos V= \frac{TV}{UV}[/tex]
[tex]cos\ V = \frac{6}{3\sqrt{29}}[/tex]
[tex]cos\ V = \frac{2}{\sqrt{29}}[/tex]
Rationalize:
[tex]cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]cos\ V = \frac{2\sqrt{29}}{29}[/tex]
