Question

Find the cosine of ∠X.
20
48
52
X
Y
W
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cos(X)=

Answer 1

To find the cosine of angle \( \angle X \) in a triangle, we can apply the cosine definition in the context of a right triangle. Based on the numbers you provided (20, 48, and 52), it seems like there may be a right triangle involved.

We can check if these numbers form a right triangle using the Pythagorean theorem, where:

\[
a^2 + b^2 = c^2
\]

For our case:

- Let \( a = 20 \)
- Let \( b = 48 \)
- Let \( c = 52 \)

Now let's check:

\[
20^2 + 48^2 = 400 + 2304 = 2704
\]
\[
52^2 = 2704
\]

Since both sides are equal, we confirm that we indeed have a right triangle, where \( c = 52 \) is the hypotenuse.

The cosine of angle \( \angle X \) (assuming it is opposite the side of length 20) is defined as:

\[
\cos(X) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]

In this case, we can take:

- The adjacent side to \( \angle X \) is \( 48 \),
- The hypotenuse is \( 52 \).

Thus,

\[
\cos(X) = \frac{48}{52}
\]

Now we simplify \( \frac{48}{52} \):

Both 48 and 52 can be divided by 4:

\[
\cos(X) = \frac{48 \div 4}{52 \div 4} = \frac{12}{13}
\]

So, the final answer for \( \cos(X) \) is:

\[
\cos(X) = \frac{12}{13}
\]