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
opposite
∠XX and
adjacent to
∠WW .
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Answer 1

To express the trigonometric ratios as fractions in simplest terms, let's denote the sides of the triangle:

- \( V \) is the length of the opposite side to angle \( X \),
- \( W \) is the length of the adjacent side to angle \( W \),
- The hypotenuse is the longest side \( H \).

From the information given, we have:

- \( V = 14 \)
- \( W = 48 \)
- The hypotenuse can be found using the Pythagorean theorem:

\[
H = \sqrt{V^2 + W^2} = \sqrt{14^2 + 48^2} = \sqrt{196 + 2304} = \sqrt{2500} = 50
\]

Now we can calculate the sine and cosine ratios:

1. **Sine of angle \( X \)**:

\[
\sin X = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{V}{H} = \frac{14}{50}
\]

We can simplify \( \frac{14}{50} \):

\[
\frac{14}{50} = \frac{7}{25}
\]

So,

\[
\sin X = \frac{7}{25}
\]

2. **Cosine of angle \( W \)**:

\[
\cos W = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{W}{H} = \frac{48}{50}
\]

We can simplify \( \frac{48}{50} \):

\[
\frac{48}{50} = \frac{24}{25}
\]

So,

\[
\cos W = \frac{24}{25}
\]

Now we have the final answers:

- \( \sin X = \frac{7}{25} \)
- \( \cos W = \frac{24}{25} \)

These ratios illustrate that:

\[
\sin X \text{ and } \cos W
\]
are not equal, because they represent different angles and sides of the triangle.