The smallest angle of elevation that a ladder can make with a wall and still be safe is 75 degrees. Would a ladder that’s is placed 2m from a wall and reaches 6m be considered safe.

Answer 1

To determine if the ladder is safe, we can use trigonometry to calculate the angle of elevation at which the ladder is placed.

Let x be the angle of elevation. We can use the tangent function to find x:

tan(x) = opposite/adjacent
tan(x) = 6/2
tan(x) = 3

Taking the arctan of both sides, we find:

x = arctan(3)
x ≈ 71.57 degrees

Since the angle of elevation is less than the smallest safe angle of 75 degrees, the ladder is considered safe in this scenario.