A ladder is 3.5 m long. It leans against a vertical wall when placed on horizontal ground . The ladder rest at a point on the wall that is 3m above the ground. What angle will the ladder make with the horizontal?
SinTheta=3/3.5
theta=arcsin(3/3.5)
To find the angle that the ladder makes with the horizontal, we can use trigonometry. Specifically, we can use the tangent function.
We are given that the ladder is 3.5 meters long and that it rests against a vertical wall. Let's call the angle that the ladder makes with the horizontal θ. The side opposite to θ is the height of the wall, which is 3 meters. The side adjacent to θ is the distance along the ground from the base of the ladder to the wall (the ladder itself), which is 3.5 meters.
Now, we can use the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = 3/3.5
To find the value of θ, we can take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
θ = arctan(3/3.5)
Using a calculator, we find that θ is approximately 41.49 degrees.
Therefore, the angle that the ladder makes with the horizontal is approximately 41.49 degrees.