Digital SATMath: Geometry and TrigonometryMedium
A surveyor needs to determine the height of a flagpole. From a point on the ground 20 meters away from the base of the flagpole, the angle of elevation to the top of the flagpole is measured to be 30°. Approximately what is the height of the flagpole?
- A17.3 meters
- B11.5 meters
- C10.0 meters
- D34.6 meters
Show answer & explanationAnswer & explanation
Correct answer: B. 11.5 meters
This forms a right triangle. The distance from the base is the adjacent side (20m), the height of the flagpole is the opposite side (h), and the angle is 30°. The tangent function relates opposite and adjacent: tan(angle) = opposite/adjacent. So, tan(30°) = h/20. Solving for h: h = 20 * tan(30°). Since tan(30°) ≈ 0.577, h ≈ 20 * 0.577 = 11.54 meters.
Why the other options are wrong
- A. This would be 20 * tan(60°), or 20 * sqrt(3), which is incorrect for a 30° angle.
- C. This might come from using sin(30°) with the adjacent side, or a miscalculation.
- D. This is approximately 2 * 17.3, or 2 * 20 * tan(60°), which is far too high.
Tangent Ratio (Trigonometry)
In a right-angled triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
- Formula: tan(θ) = Opposite / Adjacent
- Used to find unknown side lengths or angles in right triangles.
- Part of the SOH CAH TOA mnemonic.
Memory trick: SOH CAH TOA helps you pick the right ratio for sides and angles.