To find the distance between the two walls, we need to calculate the horizontal distances from point A to points B and C, respectively.
1. Calculate Horizontal distance from A to B:
- We know that ray AB makes an angle of \(60^\circ\) with the ground.
- The length of AB is 60m.
Using the cosine function to find the horizontal distance to wall 1 (point B): \[ d_{AB} = AB \cdot \cos(60^\circ) \] \[ d_{AB} = 60 \cdot 0.5 = 30 \text{ m} \]
2. Calculate Horizontal distance from A to C:
- The height of point C is 40m, and ray AC makes an angle of \(45^\circ\) with the ground.
We can use the sine function to find the length of ray AC: Using the opposite side (height) and the angle \(45^\circ\): \[ h_C = AC \cdot \sin(45^\circ) \] Since we know the height \(h_C = 40m\): \[ 40 = AC \cdot \frac{\sqrt{2}}{2} \] Solving for AC: \[ AC = 40 \cdot \frac{2}{\sqrt{2}} = 40\sqrt{2} \approx 56.57 \text{ m} \]
Now, using the cosine function to find the horizontal distance to wall 2 (point C): \[ d_{AC} = AC \cdot \cos(45^\circ) \] \[ d_{AC} = 40\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 40 \text{ m} \]
3. Calculate the total distance between the walls:
The distance between the two walls is the total horizontal distance from point A to point C minus the distance from point A to point B: \[ \text{Distance between the walls} = d_{AB} + d_{AC} = 30 + 40 = 70 \text{ m} \]
Thus, the distance between the walls is 70 m.
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