A ladder 20 m long touches a wall at the height of 10m find the angle made by the ladder with the horizontal?
To find the angle made by the ladder with the horizontal, we can use trigonometry. The ladder, the wall, and the ground form a right triangle.
Let's label the angle we want to find as θ (theta), the length of the ladder as L, the height of the wall as H, and the length of the base of the triangle as B.
We know that the length of the ladder is 20 m and it touches the wall at a height of 10 m. This means H = 10 m and L = 20 m.
Using the Pythagorean theorem, we can find the length of the base B:
B^2 + H^2 = L^2
B^2 + 10^2 = 20^2
B^2 + 100 = 400
B^2 = 400 - 100
B^2 = 300
B = sqrt(300) ≈ 17.32
Now, we can determine the angle θ using the trigonometric function tangent (tan):
tan(θ) = H / B
tan(θ) = 10 / 17.32
θ = arctan(10 / 17.32)
By using a scientific calculator or computer, we can find the arctan(10 / 17.32) ≈ 30 degrees.
Therefore, the angle made by the ladder with the horizontal is approximately 30 degrees.