Final answer:
Using trigonometry, the angle of elevation formed by the ladder and the ground is found to be approximately 66.42 degrees by calculating the arccosine (inverse cosine) of 0.4, which is the ratio of the adjacent side (4 feet) to the hypotenuse (10 feet).
Step-by-step explanation:
To find the angle of elevation formed by the ladder and the ground, we can use trigonometry. We have a right-angled triangle with the ladder as the hypotenuse (10 feet long) and the distance from the base of the house to the bottom of the ladder as one of the sides adjacent to the angle (4 feet).
We will use the cosine function, which is defined as adjacent/hypotenuse in a right-angled triangle. The cosine of the angle of elevation (θ) can thus be calculated as follows:
cos(θ) = adjacent/hypotenuse
cos(θ) = 4 feet / 10 feet
θ = cos⁻¹(0.4)
Using a calculator, we find that the angle of elevation is approximately:
θ = cos⁻¹(0.4) ≈ 66.42 degrees
Therefore, the angle of elevation formed by the ladder and the ground is approximately 66.42 degrees.