Question

A 24 foot ladder leans against a wall so that the base of the ladder is 6 feet from the base of the building. What angle does the ladder make with the ground?

Answer 1

The ladder makes an angle of 75.52 degrees to the wall

Explanation:

Once the ladder leans against the wall, it forms a right angled triangle as shown in the attached image, with the hypotenuse being 24 feet and the adjacent side being 6 feet.

from pythagoras' theorem,

cosine θ= adjecent side/ hypotenuse side.

applying this formula, we have that

`cos \theta = (adjacent)/(hypotenuse)=(6)/(24)`

`\theta=cos^(-1)((6)/(24))= 75.52 degrees`

The angle the ladder make with the ground is 75.52 degrees?

Answer 2

77.63 degrees

Explanation:

In this question, we are asked to calculate the angle a ladder having a height of 24 foot makes with the floor if the base of the ladder is 6 feet from the base of the building.

Let’s proceed.

This is a pretty straightforward question. To calculate the angle, we first need to identify that the length of the ladder would stand for the hypotenuse of the right angle triangle formed by the ladder and the wall. While, the distance of 6 foot stands for the adjacent.

Since we are having a comparison between hypotenuse and adjacent, the trigonometric identity to use is the cosine.

Mathematically, cosine Theta = adjacent/hypotenuse

Cosine theta = 6/28

Cosine theta = 0.2143

Theta = arc.cosine 0.2143

Theta = 77.63 degrees

Please check attachment for diagram