Question

Express cos WW as a fraction in simplest terms.
U
V
W
8
6
Answer
Attempt 1 out of 2

Answer 1

To express \( \cos WW \) as a fraction in simplest terms, we first need to determine the value of \( W \).

Given that:
- \( U = 8 \)
- \( V = 6 \)

The values of \( U \) and \( V \) suggest a simple relationship to angles, since \( U \) and \( V \) are both lengths. We can express \( W \) in terms of \( U \) and \( V \).

Suppose we define \( W \) as the angle in radians or degrees corresponding to some geometrical setup, such as a right triangle where \( U \) and \( V \) are the lengths of two sides.

If we assume \( W \) is an angle in a right triangle and we want to find \( \cos W \), we can use:

\[
W = \tan^{-1}\left(\frac{V}{U}\right) = \tan^{-1}\left(\frac{6}{8}\right) = \tan^{-1}\left(\frac{3}{4}\right)
\]

### Calculating \( \cos W \):
Now, using the definitions:

For a right triangle with sides \( U \) (adjacent to angle \( W \)) and \( V \) (opposite to angle \( W \)), we can calculate the hypotenuse \( H \):

\[
H = \sqrt{U^2 + V^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10
\]

Now, the cosine of the angle \( W \) is given by the ratio:

\[
\cos W = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{U}{H} = \frac{8}{10} = \frac{4}{5}
\]

Thus, \( \cos W = \frac{4}{5} \).

So, the answer is:

\[
\cos WW = \frac{4}{5}
\]