Question

A ladder 8.5 meters long leans against a vertical wall. The top (T) of the ladder makes an angle of 58 degrees with the wall. How far, correct to one decimal place, is the foot of the ladder from the wall?

A) 6.1 meters
B) 7.2 meters
C) 6.9 meters
D) 8.0 meters

Answer 1

Using trigonometry and the cosine function, we can calculate that the distance from the foot of the ladder to the wall is approximately 4.5 meters when the ladder is 8.5 meters long and makes a 58-degree angle with the wall.

Step-by-step explanation:

To calculate how far the foot of the ladder is from the wall given the length of the ladder and the angle it makes with the wall, we can use trigonometry. Specifically, we can use the cosine function which relates the adjacent side (distance from foot to wall), the hypotenuse (length of ladder), and the angle between hypotenuse and adjacent.

Let's use the following steps:

1. Identify the angle (θ) which is given as 58 degrees.
2. Identify the length of the ladder (L) which is 8.5 meters.
3. Use the cosine function: cos(θ) = adjacent/hypotenuse = distance from the wall (D)/L.
4. Plug in the known values and solve for D: cos(58°) = D/8.5 m.
5. Compute the value of D which will be D = cos(58°) × 8.5 m.

Using a calculator, we find that cos(58°) ≈ 0.5299. Therefore, D ≈ 0.5299 × 8.5 m ≈ 4.5 meters.