- Math »
- 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

You can find the length of the ladder, which is leaning against the wall, in this problem by using the trigonometric function 'cosine'.

by Ashnath Jeba

**Updated **Mar 18, 2024

**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

## The Angle of Elevation of a Ladder Leaning Against a Wall is 60° - FAQs

1. How do you calculate the length of a ladder leaning against a wall?

To calculate the length of a ladder leaning against a wall, you can use the trigonometric function cosine (cos).

2. What is the angle of elevation of the ladder in this problem?

The angle of elevation of the ladder is 60 degrees.

3. Why is cosine used in this ladder problem?

Cosine is used in this problem because the adjacent side is known and we need to find the length of the hypotenuse.

## Recent Updates

- Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
- Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading...
- Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
- P and S can complete a piece of work in 20 and 15 days respectively. They worked togeth...
- Each day that a library book is kept past its due date, a $0.30 fee is charged at midni...
- Teri goes shopping for some new clothes and then out to lunch with a friend. She spends...
- Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the...
- A and B stand at distinct points of a circular race track of length 135 m. They cycle a...
- The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a ...
- In pea plants, Tall plant height is dominant over short plant height. If there are 200 ...
- A wall of length 10 m was to be built across an open ground. The height of the wall is ...
- A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Mr. ...
- In a forest 20% of Mushrooms are Red, 50% Brown and 30% White. A Red mushroom is poison...
- In a large population, 76% of the households own microwaves. A simple random sample of ...
- A bag contains 8 red marbles, 9 yellow marbles, 7 green marbles. How many additional re...