By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.
Will the ladder be safe at this height?
Notice that the ladder makes a right triangle with the wall.
Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft
If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.
Then we can use the relation:
sin(x) = (opposite cathetus)/(hypotenuse)
Then:
sin(x) = (13.5ft)/(15ft)
If we use the inverse sine function on both sides, we get:
Asin(sin(x)) = Asin( 13.5ft/15ft)
x = Asin(13.5/15) = 64.2°
So the angle is less than 75°, which means that in fact, the ladder is safe.
If you want to learn more about right triangles:
https://brainly.com/question/2217700
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