To determine the length of the side opposite the 25° angle in the second triangle with a hypotenuse of length 10, we can use the sine function.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we can express this relationship mathematically:
\[ \sin(25^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} \]
For the second triangle:
- Hypotenuse = 10
- Opposite side (what we want to find) = \( x \)
Inserting the values, we have:
\[ \sin(25^\circ) = \frac{x}{10} \]
To find \( x \), we rearrange this equation:
\[ x = 10 \cdot \sin(25^\circ) \]
Next, we can calculate \( \sin(25^\circ) \). Using a calculator, we find:
\[ \sin(25^\circ) \approx 0.4226 \]
Now substituting this value back into the equation for \( x \):
\[ x \approx 10 \cdot 0.4226 \approx 4.226 \]
Rounding this, we find:
\[ x \approx 4 \]
Therefore, the length of the side opposite the 25° angle in the second triangle is \( \boxed{4} \).
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