To find the length of the side opposite the 25-degree angle in the second triangle, we can use the relationship between the side lengths and the angles in a right triangle.
In a right triangle, given an angle \(\theta\) and the length of the hypotenuse \(c\), the length of the side opposite the angle can be calculated using the sine function: \[ \text{opposite} = c \cdot \sin(\theta) \]
For the second triangle, we have:
- The hypotenuse \(c = 10\)
- The angle \(\theta = 25\) degrees
Therefore, the length of the side opposite the 25-degree angle in the second triangle is: \[ \text{opposite} = 10 \cdot \sin(25^\circ) \]
Now, we can calculate \(\sin(25^\circ)\). Using a calculator: \[ \sin(25^\circ) \approx 0.4226 \]
Substituting this value into the equation: \[ \text{opposite} \approx 10 \cdot 0.4226 = 4.226 \]
Thus, the length of the side opposite the 25-degree angle in the second triangle is approximately: \[ \boxed{4.23} \]
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