A ladder 20m long rest against a vertical wall so that the foot of the ladder is 9m long. Find correct to the nearest degree the angle that the ladder makes with the wall.
sinα =9/20 =0.45
α=sin⁻¹0.45 =26.7⁰
To find the angle that the ladder makes with the wall, we can use trigonometric functions. In this case, we can use the sine function.
Let's label the length of the ladder (hypotenuse) as 'H' and the distance of the foot of the ladder from the wall as 'A'. We are given that H = 20m and A = 9m.
Using the Pythagorean theorem, we can find the height (opposite side) of the triangle formed by the ladder and the wall:
H^2 = A^2 + O^2
20^2 = 9^2 + O^2
400 = 81 + O^2
O^2 = 400 - 81
O^2 = 319
O ≈ √319
Now that we know the lengths of the opposite and adjacent sides of the triangle, we can use the sine function to calculate the angle:
sinθ = O / H
sinθ = (√319) / 20
θ ≈ sin^(-1)((√319) / 20)
Using a scientific calculator or trigonometric tables, we can find the angle (θ) to the nearest degree. From the calculations, we find that θ ≈ 53 degrees.
So, the angle that the ladder makes with the wall is approximately 53 degrees.