Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A technician is installing a new antenna mast. To stabilize the mast, two guy wires are attached from the top of the 24-foot mast to the ground. Each wire makes an angle of 60 degrees with the ground. What is the approximate total length of both guy wires needed?
- A48 feet
- B96 feet
- C55.4 feet
- D27.7 feet
Show answer & explanationAnswer & explanation
Correct answer: C. 55.4 feet
This problem involves trigonometry, specifically the sine function. The mast height is the opposite side to the 60-degree angle, and the guy wire is the hypotenuse. Since sin(θ) = opposite/hypotenuse, we have sin(60°) = 24 / hypotenuse. Solve for the hypotenuse (length of one wire) and then multiply by 2 for both wires. (sin 60° ≈ 0.866).
Why the other options are wrong
- A. This is the length of two wires if the angle was 30 degrees or a miscalculation.
- B. This is incorrect; it might be related to using an incorrect trigonometric function or an incorrect base calculation.
- D. This is the length of one wire if calculated with cosine or an incorrect angle.
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 – 'Some Old Hippie, Caught Another Hippie, Tripping On Acid'!