A ladder of length 6m leans against a vertical wall so that the base of the ladder is 2mm from the wall. What is the angle between the ladder and the wall?
The length of the ladder is 6m. Let the angle between the ladder and the wall be A.
The base of the ladder is 2 mm away from the wall.
As we know the distance of the ladder from the wall and its length, we can calculate the sine of the angle A.
sin A = (2/1000)/6
=> sin A = 1/3000
A = arc sin (1/3000)
=> A = 0.019 degrees
The angle between the wall and the ladder is 0.019 degrees.
The length of the ladder represents the hypotenuse of the right angle triangle, whose legs are the vertical wall from the top of the ladder to the floor and the floor between the wall and the base of the ladder.
Since the length of the base is opposite to the angle that has to be computed, we'll use the sine function to find out the measure of the angle.
Let the angle be t:
sin t = 2/6*1000
sin t = 1/3000
t = arcsin (1/3000)
t = 0.017 degrees
The requested angle between the ladder and the wall is t = 0.017 degrees.