A building is 50 m tall. If a person standing 40 m away from the building sees t

A building is 50 m tall. If a person standing 40 m away from the building sees the top at an angle of elevation of θ, what is the value of θ? (2021)

A building is 50 m tall. If a person standing 40 m away from the building sees the top at an angle of elevation of θ, what is the value of θ? (2021)

Step 1: Identify the height of the building, which is 50 meters.
Step 2: Identify the distance from the person to the building, which is 40 meters.
Step 3: Understand that the angle of elevation (θ) is the angle formed between the line of sight to the top of the building and the horizontal line from the person to the base of the building.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building). The formula is tan(θ) = height/distance.
Step 5: Substitute the values into the formula: tan(θ) = 50/40.
Step 6: Simplify the fraction: 50/40 = 1.25.
Step 7: To find θ, use the inverse tangent function: θ = tan⁻¹(1.25).
Step 8: Calculate θ using a calculator: θ ≈ 53.13 degrees.

Trigonometry – The problem involves using the tangent function to relate the height of the building and the distance from the observer to find the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for solving problems involving heights and distances.