A ladder 10 m long reaches a window 8 m high. What is the angle of elevation of

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Question: A ladder 10 m long reaches a window 8 m high. 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, sin(θ) = 8/10, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

A ladder 10 m long reaches a window 8 m high. What is the angle of elevation of the ladder from the ground? (2019)

A ladder 10 m long reaches a window 8 m high. What is the angle of elevation of the ladder from the ground? (2019)

Step 1: Identify the lengths involved. The ladder is 10 m long (hypotenuse) and the height of the window is 8 m (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 = sin⁻¹(0.8).
Step 6: Calculate the angle using a calculator: θ ≈ 53.13 degrees.

Trigonometric Ratios – Understanding how to use sine, cosine, and tangent to find angles and lengths in right triangles.
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.