A ladder 10 meters long reaches a window 8 meters high. What is the angle of ele

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Question: A ladder 10 meters long reaches a window 8 meters high. 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) = 8/10, θ = arcsin(0.8) = 53.13 degrees.

A ladder 10 meters long reaches a window 8 meters high. What is the angle of elevation of the ladder from the ground?

A ladder 10 meters long reaches a window 8 meters high. 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 meters long (hypotenuse) and the height of the window is 8 meters (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) = 8/10.
Step 4: Simplify the fraction: sin(θ) = 0.8.
Step 5: To find the angle θ, use the inverse sine function: θ = arcsin(0.8).
Step 6: Calculate the angle using a calculator: θ ≈ 53.13 degrees.

Trigonometry – The use of sine function to find angles in right triangles.
Right Triangle Properties – Understanding the relationship between the sides and angles in a right triangle.