Question

A ladder 20m long leans against a vertical wall such that it makes an angle of 30° with the horizontal ground. Calculate, to one decimal place, the distance of the foot of the ladder from the wall.

a) 10.0 m
b) 17.3 m
c) 20.0 m
d) 34.6 m

Answer 1

To find the distance from the wall to the bottom of the ladder, we used the cosine function with the given 30° angle and the ladder's length of 20 m. The calculation results in a distance of approximately 17.3 m, corresponding with option b).

Step-by-step explanation:

To calculate the distance of the foot of the ladder from the wall, we use trigonometric ratios. In this case, a ladder makes a 30° angle with the horizontal ground. By using the cosine function, which relates the adjacent side (distance from the wall to the ladder's bottom) to the hypotenuse (ladder's length), we can find the desired distance.

The formula using the cosine function is:

cos(θ) = adjacent/hypotenuse

Plugging the values into the formula:

cos(30°) = distance from the wall / 20 m

Using the exact value for cos(30°), which is √3/2, the equation becomes:

(√3/2) = distance from the wall / 20 m

Multiplying both sides by 20 m, we get:

distance from the wall = 20 m * (√3/2)

Calculating this, we get:

distance from the wall = 20 m * (0.866) ≈ 17.3 m

Therefore, the distance of the foot of the ladder from the wall is approximately 17.3 m, which corresponds to option b).