A ladder 10 m long reaches a window 8 m above the ground. What is the angle of elevation of the ladder from the ground?
Correct Answer: 53.13 degrees
- Step 1: Identify the lengths involved. The ladder is 10 m long (hypotenuse) and the height of the window is 8 m (opposite side).
- Step 2: Use the sine function to relate the angle of elevation (θ) to the opposite and hypotenuse sides. The formula is sin(θ) = opposite/hypotenuse.
- Step 3: Substitute the known values into the formula: sin(θ) = 8/10.
- Step 4: Simplify the fraction: sin(θ) = 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.
- Trigonometric Ratios – Understanding the relationship between the angles and sides of a right triangle, specifically using sine to find angles.
- Right Triangle Properties – Recognizing the right triangle formed by the ladder, the wall, and the ground.
