a ladder 24m rest against the vertical one so that distance between the foot for the ladder and the wall is 8m. Find to the nearest dega the angle. The ladder makes with the wall.
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To find the angle that the ladder makes with the wall, we can use trigonometry. Let's call the angle θ.
In this scenario, we have a right-angled triangle formed by the ladder, the distance between the foot of the ladder and the wall (8m), and the height of the ladder (24m). We can use the tangent function to find the angle θ.
The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the side opposite θ is the height of the ladder (24m), and the side adjacent to θ is the distance between the foot of the ladder and the wall (8m).
So, the tangent of θ can be calculated as:
tan(θ) = opposite/adjacent
tan(θ) = 24/8
tan(θ) = 3
Now, we need to find the value of θ. We can do this by taking the inverse tangent (or arctan) of both sides:
θ = tan^(-1)(3)
Using a calculator, we can find the inverse tangent of 3, which is approximately 71.57 degrees.
Therefore, the angle the ladder makes with the wall is approximately 71.57 degrees.