A ladder 20 meters long reaches a window 16 meters above the ground. What is the

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Question: A ladder 20 meters long reaches a window 16 meters above the ground. What is the angle of elevation of the ladder from the ground?

Options:

Correct Answer: 60 degrees

Solution:

Using sin(θ) = opposite/hypotenuse, sin(θ) = 16/20, θ = sin⁻¹(0.8) ≈ 60 degrees.

A ladder 20 meters long reaches a window 16 meters above the ground. What is the angle of elevation of the ladder from the ground?

A ladder 20 meters long reaches a window 16 meters above the ground. What is the angle of elevation of the ladder from the ground?

Correct Answer: 60 degrees

Step 1: Identify the lengths involved. The ladder is 20 meters long (this is the hypotenuse) and the height of the window is 16 meters (this is the opposite side).
Step 2: Use the sine function to find the angle of elevation. The formula is sin(θ) = opposite/hypotenuse.
Step 3: Substitute the known values into the formula: sin(θ) = 16/20.
Step 4: Simplify the fraction: 16/20 = 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 ≈ 60 degrees.

Trigonometry – The question tests the understanding of basic trigonometric functions, specifically the sine function, to find the angle of elevation.
Right Triangle Properties – It involves recognizing the relationship between the sides of a right triangle formed by the ladder, the wall, and the ground.