Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A construction worker is building a ramp. The ramp rises 3 feet vertically for every 4 feet of horizontal distance. What is the angle of elevation of the ramp to the nearest degree?
- A37°
- B53°
- C30°
- D45°
Show answer & explanationAnswer & explanation
Correct answer: A. 37°
This scenario forms a right-angled triangle where the vertical rise is the opposite side and the horizontal distance is the adjacent side to the angle of elevation. The tangent of the angle (θ) is opposite/adjacent, so tan(θ) = 3/4 = 0.75. To find the angle, we use the inverse tangent function: θ = arctan(0.75). Using a calculator, arctan(0.75) ≈ 36.87°, which rounds to 37°.
Why the other options are wrong
- B. Incorrect; tan(53°) ≈ 1.327.
- C. Incorrect; tan(30°) ≈ 0.577.
- D. Incorrect; tan(45°) = 1.
Angle of Elevation (Trigonometry)
The angle formed by the horizontal line of sight and the upward line of sight to an object.
- Often involves a right-angled triangle.
- Related to trigonometric ratios: sine, cosine, tangent.
- Use inverse trigonometric functions (arcsin, arccos, arctan) to find the angle.
Memory trick: SOH CAH TOA: Say it often, helps you know, which ratio for which side to go!