A 36 ft. ladder is used to reach the top of 28ft. wall. If the ladder extends 2 ft. from the top of the wall, find its inclination to the horizontal.
The ladder is represented by the hyp.
of a rt triangle. The wall is represented by the ver. side of rt.
triangle. In our calculation, 34 ft. will be used for the hyp. because 2
ft. of the ladder extends above wall.
CosA = 28 / 34 =0.8235, A = 34.6 Deg. = Angle of inclination.
draw the figure
A 36 ft. ladder is used to reach the top of a 28 ft. wall. If the ladder extends 2 ft. past the top of the wall , Find its inclination to the horizontal.
To find the inclination of the ladder to the horizontal, we can use the tangent function.
Let's consider the ladder as the hypotenuse of a right triangle, with the vertical distance from the top of the wall to the ground as the opposite side and the horizontal distance from the base of the wall to the ladder as the adjacent side.
The opposite side is the height of the wall, which is given as 28 ft. The adjacent side is the distance the ladder extends beyond the top of the wall, which is given as 2 ft.
Using the Pythagorean theorem, we can find the length of the ladder as follows:
ladder^2 = height^2 + distance^2
ladder^2 = 28^2 + 2^2
ladder^2 = 784 + 4
ladder^2 = 788
ladder = square root of 788
ladder ≈ 28.08 ft
Now that we know the length of the ladder, we can calculate the inclination using the tangent function:
tangent (θ) = opposite / adjacent
tangent (θ) = height / distance
tangent (θ) = 28 / 2
tangent (θ) = 14
To find the angle (θ), we can take the inverse tangent (arctan) of the value:
θ = arctan (14)
θ ≈ 85.3 degrees
Therefore, the inclination of the ladder to the horizontal is approximately 85.3 degrees.
To find the inclination of the ladder to the horizontal, we can use trigonometry. The ladder, the distance from the top of the wall to the ground, and the horizontal form a right triangle.
Let's denote the length of the ladder as "L" (36 ft), the height of the wall as "H" (28 ft), and the distance from the top of the wall to the ground as "d" (2 ft).
We can use the Pythagorean theorem to relate the sides of the right triangle:
L^2 = H^2 + d^2
Substituting the given values, we have:
36^2 = 28^2 + 2^2
1296 = 784 + 4
1296 = 788
To isolate H, we subtract 784 from both sides:
H^2 = 1296 - 784
H^2 = 512
Now, take the square root of both sides:
H = √512
H = 22.63 ft (approximately)
Now that we know the height of the wall, we can find the inclination of the ladder to the horizontal:
Inclination = arctan(H/d)
Inclination = arctan(22.63/2)
Using a scientific calculator or trigonometric table, we can evaluate the arctan function to find the angle.
Therefore, the inclination of the ladder to the horizontal is approximately 85.04 degrees.