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

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

Solution: Using sin(θ) = opposite/hypotenuse, sin(θ) = 8/10, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Steps: 8

Step 1: Understand the problem. We have a ladder that is 10 meters long and it reaches a window that is 8 meters high.
Step 2: Visualize the situation. Imagine a right triangle where the ladder is the hypotenuse, the height of the window (8 meters) is the opposite side, and the ground is the adjacent side.
Step 3: Identify the relevant trigonometric function. We will use the sine function, which relates the angle of elevation (θ) to the opposite side and the hypotenuse.
Step 4: Write the sine formula. The formula is sin(θ) = opposite/hypotenuse. Here, opposite = 8 meters and hypotenuse = 10 meters.
Step 5: Substitute the values into the formula. This gives us sin(θ) = 8/10.
Step 6: Simplify the fraction. 8/10 can be simplified to 0.8.
Step 7: Use the inverse sine function to find the angle. We calculate θ = sin⁻¹(0.8).
Step 8: Use a calculator to find the angle. This gives us θ ≈ 53.13 degrees.