1.) To find the distance between the top of the ladder and the bottom of the window, we can use trigonometry. The ladder, the wall, and the ground form a right-angled triangle. with diagram
Given:
- The height of the window from the ground is 4 meters.
- The ladder is leaning against the wall at an angle of 60 degrees.
Let:
- The distance between the base of the ladder and the wall be x.
- The distance between the top of the ladder and the window be y.
Using trigonometry, we can use the sine function to find the length of the ladder:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 4/y
y = 4/sin(60 degrees)
y = 4/√3
y = (4√3) / 3
y = (4√3) / 3 meters
Therefore, the distance between the top of the ladder and the bottom of the window is (4√3) / 3 meters.
The diagram for this scenario would look like this:
```
/|
/ |
/ y (top of ladder to window)
4 / |
/θ |
/ |
/__________| x (base of ladder to wall)
```