Question

PLS HELPPPPPP!!!!!!!

Annie leans a 3m ladder against a wall. If the angle of elevation of the ladder is 62 degrees, how far is the ladder's base from the wall? Include a properly labeled diagram as part of your answer and round your answer to the nearest metre.

Answer 1

The ladder's base is about 1 m away from the wall.

Explanation:

• Because this is a right triangle, we're able to find the distance between the ladder's base and the wall using one of the trigonometric ratios.

• Note that the angle of elevation is made by the ladder and the ground.
• The length of the ladder (3m) is the hypotenuse in the diagram.
• When the 62° angle is the reference angle, the distance between the ladder's base and the wall is the adjacent side and the length of the ladder is the hypotenuse.

Thus, we can find the distance between the ladder's base and the wall using the cosine ratio, which is:

cos (θ) = adjacent / hypotenuse, where

• θ is the measure of the reference angle.

Thus we plug in 62 for θ and 3 for the hypotenuse in the cosine ratio, allowing us to find a, the length of the adjacent side (i.e., the distance between the ladder's base and the wall):

(cos (62) = a / 3) * 3

3 * cos (62) = a

3 * 0.4694715628 = a

1.408414688 = a

1 = a

Thus, the ladder's base is about 1 m away from the wall.

I attached a picture showing you where and how to label the diagram to represent the information.

The measurements and names we're given are in blue, the angle of elevation is purple, while the answer (and the name of it's side) is in red.

Note that there's no measurement for the wall nor the angle between the top of the ladder and the wall since we didn't need to find these measurements.