To the nearest degree what is the angle formed with the ground by a 32 ft ladder if it is leaning against a wall at a height of 28 ft?
sinØ = 28/32 = .875
Ø = appr 61°
61
To find the angle formed with the ground by the ladder, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the wall, which is 28 ft, and the adjacent side is the base of the triangle, which is the distance of the ladder from the wall.
Let's call the angle formed by the ladder and the ground θ.
Using the formula for tangent, we have:
tan(θ) = opposite/adjacent
tan(θ) = 28/unknown
Since the unknown is the distance of the ladder from the wall, let's solve for that.
Multiplying both sides by the unknown:
unknown * tan(θ) = 28
Dividing both sides by tan(θ):
unknown = 28 / tan(θ)
Now, let's calculate the value of θ.
Plug in the values into your calculator to find the value of tan^-1(28/unknown) that is closest to the answer.
After calculating, let's assume we find that tan^-1(28/unknown) is equal to 0.91 radians.
To convert radians to degrees, we need to multiply by 180/π (approximately 57.3).
θ ≈ 0.91 * (180/π) ≈ 52.4 degrees
Therefore, the angle formed with the ground by the ladder is approximately 52.4 degrees.
To find the angle formed by the ladder with the ground, we can use the inverse tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the wall (28 ft), and the adjacent side is the length of the ladder (32 ft).
Therefore, we have the equation:
tan(θ) = opposite/adjacent
tan(θ) = 28/32
To find θ, we can use the inverse tangent function (also known as atan or tan^(-1)) on both sides of the equation:
θ = atan(28/32)
Calculating this on a calculator or using a programming language that supports trigonometric functions, we find:
θ ≈ 39.80 degrees
So, to the nearest degree, the angle formed with the ground by the 32 ft ladder is approximately 40 degrees.