A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
Practice Questions
1 question
Q1
A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
12√3 m
6 m
12 m
24 m
Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
Solution: Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.
Steps: 9
Step 1: Understand the problem. We have a ladder leaning against a wall, forming a right triangle with the ground and the wall.
Step 2: Identify the given information. The distance from the foot of the ladder to the wall is 12 meters, and the angle between the ladder and the ground is 60 degrees.
Step 3: Recall the trigonometric function we will use. We will use the tangent function because we have the opposite side (height) and the adjacent side (distance from the wall).
Step 4: Write the formula for tangent. The formula is tan(angle) = opposite/adjacent.
Step 5: Substitute the known values into the formula. Here, tan(60°) = height / 12.
Step 6: Calculate tan(60°). The value of tan(60°) is √3.
Step 7: Set up the equation. We have √3 = height / 12.
Step 8: Solve for height. Multiply both sides by 12: height = 12 * √3.
Step 9: Calculate the height. The height at which the ladder touches the wall is 12√3 meters.
