Final answer:
The angle a 40 ft ladder makes with the ground, when the base is 15 ft from the building, is approximately 68.20 degrees.
Step-by-step explanation:
To calculate the angle that a ladder makes with the ground, we can use the trigonometric function of cosine since we have the length of the adjacent side (distance from the base of the ladder to the building) and the length of the hypotenuse (the ladder itself). The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.
The formula to find the angle θ is:
θ = cos-1(adjacent/hypotenuse)
In this case, adjacent = 15 ft and hypotenuse = 40 ft, which gives us:
θ = cos-1(15/40)
Using a calculator, we find that:
θ ≈ cos-1(0.375)
θ ≈ 68.20°
The angle the ladder makes with the ground to the nearest hundredth is 68.20°.