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Sagot :
Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.
What is a slope?
The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
- The angle is of 45º.
- The vertical distance is the height of h.
- The horizontal distance is of 3m.
Hence:
tan(45º) = h/3.
1 = h/3.
h = 3 m.
If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:
[tex]\tan{\theta} = \frac{2}{3}[/tex]
[tex]\theta = \arctan{\left(\frac{2}{3}\right)}[/tex]
[tex]\theta = 33.69^\circ[/tex]
More can be learned about the slope concept at https://brainly.com/question/18090623
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