Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A surveyor needs to determine the height of a flagpole. From a point on the ground 40 feet away from the base of the flagpole, the angle of elevation to the top of the flagpole is 30 degrees. How tall is the flagpole to the nearest foot?
- A23 feet
- B20 feet
- C35 feet
- D69 feet
Show answer & explanationAnswer & explanation
Correct answer: A. 23 feet
This forms a right-angled triangle where the height of the flagpole is the opposite side to the angle of elevation, and the distance from the base is the adjacent side. The tangent function relates these: tan(angle) = opposite/adjacent. So, tan(30°) = height / 40. We know tan(30°) ≈ 1/√3 ≈ 0.577. Therefore, height = 40 * tan(30°) ≈ 40 * 0.577 ≈ 23.08 feet. To the nearest foot, the height is 23 feet.
Why the other options are wrong
- B. This would be the height if the angle was 26.56 degrees or if it was 40 * sin(30).
- C. This is 40 * cos(30), which is an incorrect application of trigonometry.
- D. This is 40 / sin(30) or 40 / (1/2), which is incorrect.
Trigonometry (SOH CAH TOA)
A branch of mathematics dealing with the relationships between the sides and angles of triangles, particularly right-angled triangles.
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
Memory trick: SOH CAH TOA, your best friend for triangles, hooray!