Answered

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25.
A ladder stands against a wall at an angle of 45° to the floor. The foot of the ladder is 3 m
from the wall. If the ladder slides 1 m down the wall, then the angle between the ladder
and the floor is such that:

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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