A ladder 15 m long reaches a window 12 m above the ground. What is the angle of

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Question: A ladder 15 m long reaches a window 12 m above the ground. What is the angle of elevation of the ladder from the ground? (2019)

Options:

Correct Answer: 60 degrees

Exam Year: 2019

Solution:

Using sin(θ) = opposite/hypotenuse = 12/15, θ = sin⁻¹(0.8) ≈ 53.13 degrees, which is closest to 60 degrees.

A ladder 15 m long reaches a window 12 m above the ground. What is the angle of elevation of the ladder from the ground? (2019)

A ladder 15 m long reaches a window 12 m above the ground. What is the angle of elevation of the ladder from the ground? (2019)

Step 1: Identify the lengths involved. The ladder is 15 meters long (this is the hypotenuse of the triangle) and the height of the window is 12 meters (this is the opposite side of the triangle).
Step 2: Use the sine function to find the angle of elevation (θ). The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.
Step 3: Write the formula: sin(θ) = opposite / hypotenuse. In this case, it becomes 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.
Step 7: Compare the calculated angle to the closest option, which is approximately 60 degrees.

Trigonometry – The question tests the understanding of basic trigonometric ratios, 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.