Question

Express the trig ratios as fractions in simplest terms.
V
W
X
14
50
48
Answer
Attempt 1 out of 2

sin XX =

cos WW =

sin XX and cos WW
are equal
because start overline, V, W, end overline
VW
is
adjacent to
∠XX and
opposite
∠WW .
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Answer 1

To express the trigonometric ratios as fractions in simplest terms, let’s first analyze the triangle with the given sides:

- \(V = 14\) (length of one side)
- \(W = 50\) (length of another side)
- \(X = 48\) (length of the remaining side)

We need to identify which angles correspond to which sides. Based on the triangle layout, we can assume:

- The side opposite angle \(X\) has length \(x = 48\),
- The side opposite angle \(W\) has length \(w = 50\),
- The side opposite angle \(V\) has length \(v = 14\).

### Trigonometric Ratios

1. **Sine of angle X (\( \sin X \))**:
\[
\sin X = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Here, the opposite side of angle \(X\) is \(48\), and let's assume the hypotenuse is \(50\) (the longest side in this case):
\[
\sin X = \frac{48}{50} = \frac{24}{25}
\]

2. **Cosine of angle W (\( \cos W \))**:
\[
\cos W = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
The adjacent side of angle \(W\) is \(14\), and the hypotenuse remains \(50\):
\[
\cos W = \frac{14}{50} = \frac{7}{25}
\]

### Comparison of Sine X and Cosine W

Now we check if \( \sin X \) and \( \cos W \) are equal:
\[
\sin X = \frac{24}{25}, \quad \cos W = \frac{7}{25}
\]
Since \( \frac{24}{25} \neq \frac{7}{25} \), they are not equal.

### Final Answers

Thus we have:
- \( \sin X = \frac{24}{25} \)
- \( \cos W = \frac{7}{25} \)

If you need any further explanation or assistance, feel free to ask!