A ladder of length 6 m leans against a vertical wall so that the base of ladder is 2m from the wall. calculate the angle between the ladder and the wall.
If you want the angle between the wall and ladder it will be:
Sine inverse multiplied to 2 divided by 6
Answer is : 19.47122063
19.5 degree(rounded up)
70.5
To calculate the angle between the ladder and the wall, you can use the trigonometric function tangent (tan). The tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.
In this case, the side opposite the angle is the height of the wall that the ladder reaches, and the side adjacent to the angle is the distance from the base of the ladder to the wall. Let's call the angle θ.
Given:
Length of the ladder (hypotenuse) = 6 m
Distance from the base of the ladder to the wall = 2 m
Using the Pythagorean theorem, we can find the height of the wall.
Applying the theorem, we have:
(height of the wall)^2 + (distance from base to wall)^2 = (length of the ladder)^2
Let's plug in the given values:
(height of the wall)^2 + (2 m)^2 = (6 m)^2
(height of the wall)^2 + 4 m^2 = 36 m^2
(height of the wall)^2 = 36 m^2 - 4 m^2
(height of the wall)^2 = 32 m^2
height of the wall = √(32 m^2)
height of the wall ≈ 5.65 m
Now that we have the height of the wall and the distance from the base to the wall, we can calculate the tangent of the angle θ:
tan(θ) = (height of the wall) / (distance from base to wall)
tan(θ) = 5.65 m / 2 m
Calculating this ratio:
tan(θ) ≈ 2.83
To find the angle θ, we need to take the inverse tangent (arctan) of this value:
θ ≈ arctan(2.83)
θ ≈ 68.5°
Therefore, the angle between the ladder and the wall is approximately 68.5 degrees.
Did you make a sketch?
If so, you can see that
cosØ = 2/6 = 1/3
Ø = cos^-1 (1/3) = appr 70.5°