A ladder 10 meters long leans against a wall, forming an angle of 60 degrees wit

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What’s inside this PDF?

Question: A ladder 10 meters long leans against a wall, forming an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

Options:

5 meters
8.66 meters
10 meters
7.5 meters

Correct Answer: 8.66 meters

Solution:

Using sin(60°) = height / ladder length, we have height = ladder length * sin(60°) = 10 * (√3/2) = 5√3 ≈ 8.66 meters.

A ladder 10 meters long leans against a wall, forming an angle of 60 degrees wit

Practice Questions

A ladder 10 meters long leans against a wall, forming an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

5 meters
8.66 meters
10 meters
7.5 meters

Questions & Step-by-Step Solutions

A ladder 10 meters long leans against a wall, forming an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

Step 1: Understand that the ladder forms a right triangle with the ground and the wall.
Step 2: Identify the length of the ladder, which is 10 meters.
Step 3: Note the angle between the ladder and the ground, which is 60 degrees.
Step 4: Recall the sine function in a right triangle: sin(angle) = opposite side (height) / hypotenuse (ladder length).
Step 5: Set up the equation using the sine of 60 degrees: sin(60°) = height / 10.
Step 6: Find the value of sin(60°), which is √3/2.
Step 7: Substitute sin(60°) into the equation: √3/2 = height / 10.
Step 8: Multiply both sides by 10 to solve for height: height = 10 * (√3/2).
Step 9: Simplify the equation: height = 5√3.
Step 10: Calculate the approximate height: 5√3 is about 8.66 meters.

Trigonometry – The use of sine function to find the height of the ladder based on the angle and length.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the ladder, wall, and ground.

A ladder 10 meters long leans against a wall, forming an angle of 60 degrees wit

What’s inside this PDF?

A ladder 10 meters long leans against a wall, forming an angle of 60 degrees wit

Practice Questions

Questions & Step-by-Step Solutions

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