The Angle of Elevation of a Ladder Leaning Against a Wall is 60° and the Foot of the Ladder is 4.6 m Away From the Wall. The Length of the Ladder is

The Angle of Elevation of a Ladder Leaning Against a Wall is 60° and the Foot of the Ladder is 4.6 m Away From the Wall. The Length of the Ladder is

In this problem, you need to find the length of the ladder which is inclined in a wall. Here is a diagrammatic representation:

Let AB be the ladder and the length of the ladder be x m.

Length from the foot of the ladder to the wall, BC = 4.6 m

To find AB, you need to use the ‘cosine’ function.

Cos θ = Adjacent side / Hypotenuse.

Cos 60° = 4.6 / x

1 / 2 = 4.6 / x

x = 4.6 (2)

x = 9.2

So, the length of the ladder is 9.2 m.

Method Explanation

In this problem, we have used the trigonometric function 'cosine' to determine the length of the ladder. For solving the problem easily, we have used a diagrammatic representation. Based on the diagram, we know the length of the adjacent side to the angle and we need find the length of the hypotenuse. To find it, we used the cosine function. Cosine relates the adjacent side to the hypotenuse.

With the help of the formula "Cos θ = Adjacent side / Hypotenuse" we have determined the length of the ladder. Here, the value of 'θ' (Angle of elevation) is 60°. It is known that the value of Cos 60° is 1 / 2. By substituting this value, we have easily solved this problem.

What is Cosine Function in Trigonometry?

Cosine (cos) is a trigonometric function that relates the adjacent side of an angle to the hypotenuse in a right-angled triangle. We use this function to solve problems involving angles and distances in right-angled triangles. In a right-angled triangle, cos is the ratio of the length of the adjacent side to that of the hypotenuse. For an angle θ, cosine function can be denoted as "Cos θ".

Here are the values of cosine degrees:

cos 0° = 1
cos 30° = √3/2
cos 45° = 1/√2
cos 60° = 1/2
cos 90° = 0
cos 120° = -1/2
cos 150° = -√3/2
cos 180° = -1
cos 270° = 0
cos 360° = 1