Estimating the Height of the Library Arch Using Trigonometry
This project presents a method for determining the height of the library arch, estimated to be around 33.28 feet. Each participant employed different angles to measure the top of the arch with a clinometer. We utilized trigonometric concepts, particularly those related to special right triangles, to calculate the height from these measurements. The various calculations involved determining the values for opposite and adjacent sides, applying the tangent function, and ultimately averaging the results to reach a consistent height estimate for the arch.
Estimating the Height of the Library Arch Using Trigonometry
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Presentation Transcript
HOW TALL IS IT? By: Kenneth Casey, Braden Pichel, Sarah Valin, Bailey Gray 1st Period – March 8, 2011
Kenneth Casey 1st 30˚ Trigonometry Opposite 30˚ is X. Adjacent 30˚ is 36 feet. Tangent= Opposite÷Adjacent. Tan 30˚= X÷36 feet. Tan (30) 36 = 20.78 ft. 20.78 ft + 5.83 ft = 26.61 ft. Special right triangles Long leg= short leg √3 36=x√3 (36/√3) = (x√3/√3) X=(36/√3) (√3/√3) X=36√3/3 X=12√3=20.78ft. 20.78 ft + 5.83 ft = 26.61 ft. 60˚ X 30˚ 5.83ft. 36 ft.
45˚ - Sarah Valin • Special Right Triangles- • leg = leg • x = 48 • 48 ft + 5.75 ft = 53.75 ft • Trig- • Tan 45° = x/48 • x = 48 • 48 ft + 5.75 ft = 53.75 ft 45° x 45° 90° 48 ft 5.75 ft
60° - Bailey Gray 30° x 60° 90° 12 ft 4.9 ft Special Right Triangles (30-60-90) : l.leg = sh.leg √3 x = 12 √3 ≈20.78 20.78 ft + 4.9 ft = 25.68 ft Trig: tan 60° = x/12 x ≈ 20.78 20.78 ft + 4.9 ft = 25.68 ft
Braden Pichel 1st 20⁰ Y X 20⁰ 60 5.25 5.25 Cos20 = 60/yCos20(y) = 60 y = 60/Cos20 y ≈ 63.85 ft. Tan20 = x/60x = Tan20(60) x ≈ 21.84 ft. Height = x + 5.25 Height = 21.84 + 5.25 Height ≈ 27.09 ft.
CONCLUSION We learned that the average height of the library arch is about 33.28 feet high. To figure this out, each person measured the top of the arch from a different angle using a clinometer. Then, we each figured out the height by using the formulas for a special right triangle and/or using trigonometry, depending on which angle was measured. After, we added the total heights each person got for their triangle, then divided by 4 to get out average height for the library arch.
