A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?
Practice Questions
1 question
Q1
A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?
30 degrees
45 degrees
60 degrees
75 degrees
Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?
Solution: Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.
Steps: 6
Step 1: Identify the lengths involved. The ladder is 15 meters long (this is the hypotenuse) and the height of the window is 12 meters (this is the opposite side).
Step 2: Use the sine function to relate the angle of elevation (θ) to the opposite side and the hypotenuse. The formula is sin(θ) = opposite/hypotenuse.
Step 3: Substitute the known values into the formula: sin(θ) = 12/15.
Step 4: Simplify the fraction: 12/15 = 0.8.
Step 5: To find the angle θ, use the inverse sine function: θ = sin⁻¹(0.8).
Step 6: Calculate θ using a calculator: θ ≈ 53.13 degrees.
