The problem requires us to find the lengths of sides $b$ and $c$ in a right-angled triangle ABC, where angle $C = 25^\circ$, side $a = 45$ m, and angle $A = 90^\circ$.

1. Problem Description

The problem requires us to find the lengths of sides $b$ and $c$ in a right-angled triangle ABC, where angle $C = 25^\circ$, side $a = 45$ m, and angle $A = 90^\circ$.

2. Solution Steps

We are given a right triangle with hypotenuse $a = 45$ meters, angle $C = 25^\circ$, and we need to find the lengths of side $b$ and side $c$.

We can use trigonometric functions to solve this problem.

Since we know the hypotenuse and the angle C, we can use the sine and cosine functions.

$$\sin(C) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{c}{a}$$

$$\cos(C) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{a}$$

Using the sine function:

$$\sin(25^\circ) = \frac{c}{45}$$

$$c = 45 \cdot \sin(25^\circ)$$

Using a calculator, we find that $\sin(25^\circ) \approx 0.4226$.

$$c \approx 45 \cdot 0.4226$$

$$c \approx 19.017$$

Using the cosine function:

$$\cos(25^\circ) = \frac{b}{45}$$

$$b = 45 \cdot \cos(25^\circ)$$

Using a calculator, we find that $\cos(25^\circ) \approx 0.9063$.

$$b \approx 45 \cdot 0.9063$$

$$b \approx 40.7835$$

3. Final Answer

The length of side $b$ is approximately $40.78$ m.

The length of side $c$ is approximately $19.02$ m.

Final Answer:

b = 40.78 m

c = 19.02 m