A ladder 20 meters long reaches a window 15 meters above the ground. What is the

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Question: A ladder 20 meters long reaches a window 15 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) = 15/20, θ = sin⁻¹(0.75) ≈ 48.6 degrees.

A ladder 20 meters long reaches a window 15 meters above the ground. What is the angle of elevation of the ladder from the ground?

A ladder 20 meters long reaches a window 15 meters above the ground. What is the angle of elevation of the ladder from the ground?

Correct Answer: 48.6 degrees

Step 1: Identify the lengths involved. The ladder is 20 meters long (hypotenuse) and the height of the window is 15 meters (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) = 15/20.
Step 4: Simplify the fraction: 15/20 = 0.75.
Step 5: To find the angle θ, use the inverse sine function: θ = sin⁻¹(0.75).
Step 6: Calculate θ using a calculator: θ ≈ 48.6 degrees.

Trigonometric Ratios – Understanding how to apply sine, cosine, and tangent ratios in right triangles to find angles and lengths.
Right Triangle Properties – Recognizing the relationship between the sides of a right triangle and the angles formed.
Inverse Trigonometric Functions – Using inverse functions to find angles when the sides of a triangle are known.