A ladder leans against a wall making a 60-degree angle with the ground. If the f

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What’s inside this PDF?

Question: A ladder leans against a wall making a 60-degree angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach on the wall?

Options:

2√3 meters
4√3 meters
4 meters
2 meters

Correct Answer: 4√3 meters

Solution:

Using sine, height = 4 * tan(60) = 4 * √3 = 4√3 meters.

A ladder leans against a wall making a 60-degree angle with the ground. If the f

Practice Questions

A ladder leans against a wall making a 60-degree angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach on the wall?

2√3 meters
4√3 meters
4 meters
2 meters

Questions & Step-by-Step Solutions

A ladder leans against a wall making a 60-degree angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach on the wall?

Step 1: Understand the problem. We have a ladder leaning against a wall, forming a 60-degree angle with the ground.
Step 2: Identify the distance from the wall to the foot of the ladder, which is 4 meters.
Step 3: Recall the relationship between the angle, the height of the ladder on the wall, and the distance from the wall. We will use the tangent function.
Step 4: The formula for tangent is: tan(angle) = opposite/adjacent. Here, the opposite side is the height we want to find, and the adjacent side is the distance from the wall (4 meters).
Step 5: Set up the equation: tan(60 degrees) = height / 4 meters.
Step 6: We know that tan(60 degrees) = √3. So, we can rewrite the equation as: √3 = height / 4.
Step 7: To find the height, multiply both sides by 4: height = 4 * √3.
Step 8: The height the ladder reaches on the wall is 4√3 meters.

Trigonometry – The problem involves using trigonometric functions (sine, cosine, tangent) to relate the angles and sides of a right triangle formed by the ladder, wall, and ground.
Right Triangle Properties – Understanding the properties of right triangles, specifically how to apply the tangent function to find the height of the ladder against the wall.

A ladder leans against a wall making a 60-degree angle with the ground. If the f

What’s inside this PDF?

A ladder leans against a wall making a 60-degree angle with the ground. If the f

Practice Questions

Questions & Step-by-Step Solutions

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