Answer:
As per the given condition: Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground.
The Orientation of the ladder with the wall forms a right triangle.
The ladder length is the hypotenuse of the triangle,
the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle,
and the height of the ladder is the vertical leg of the triangle.
⇒ Height of the ladder = 10.8 ft and hypotenuse = 13 ft
Using sine ratio formula;
[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse side}}[/tex]
Opposite side = height of the ladder = 10.8 ft and
Hypotenuse side = 13 ft.
then;
[tex]\sin \theta = \frac{10.8}{13} =0.830769230769[/tex]
or
[tex]\theta = \sin^{-1}(0.830769230769)[/tex]
Simplify:
[tex]\theta = 56.2^{\circ}[/tex] (nearest to tenth place)
Since, it is given that the angle the ladder makes with the ground needs to be 60 degree or less for safety purposes.
(a)
Yes, this ladder in a safe position.
as [tex]\theta = 56.2^{\circ} < 60^{\circ}[/tex]
(b)
You can see the diagram as shown below in the attachment.
