A 5.0m ladder is leaning 3.1m up a wall. What is the angle the ladder makes with the ground?
sinθ = 3.1/5
θ = 51.68°
Thank you steve
To find the angle the ladder makes with the ground, we can use the inverse tangent function. The opposite side of the triangle is the height of the ladder against the wall (3.1m) and the adjacent side is the distance from the base of the ladder to the wall (which is the same as the length of the ladder, 5.0m).
So, the angle θ can be found using the formula:
θ = arctan(opposite/adjacent)
θ = arctan(3.1/5.0)
Using a calculator, we can find the angle:
θ ≈ 32.26°
Therefore, the angle the ladder makes with the ground is approximately 32.26°.
To find the angle the ladder makes with the ground, we can use trigonometry. Specifically, we can use the tangent function which relates the angle to the opposite and adjacent sides of a right triangle.
In this case, the ladder forms a right triangle with the ground and the wall. The height of the triangle or the opposite side is 3.1m, and the hypotenuse of the triangle is the length of the ladder, which is 5.0m.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. Therefore, we can calculate the angle using the formula:
Tangent(angle) = Opposite/Adjacent
In our case, the opposite side is 3.1m and the adjacent side is the length of the ladder, which is 5.0m.
Tangent(angle) = 3.1/5.0
To find the angle, take the inverse tangent (also known as the arctangent) of both sides of the equation:
angle = arctan(3.1/5.0)
Use a scientific calculator or an online calculator that has the arctan function to evaluate this expression.
angle ≈ 32.18 degrees (rounded to two decimal places)
Therefore, the angle the ladder makes with the ground is approximately 32.18 degrees.