A ladder 15 meters long reaches a window 12 meters above the ground. What is the

A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?

A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?

Step 1: Identify the lengths involved. The ladder is 15 meters long (this is the hypotenuse) and the height of the window is 12 meters (this is the 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) = 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.

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