1. HOW TALL IS IT? By: Kenneth Casey, Braden Pichel, Sarah Valin, Bailey Gray 1 st Period – March 8, 2011

2. 30˚ Trigonometry 30˚ 60˚ 5.83ft. 36 ft. X 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. Kenneth Casey 1 st

3. 45 ˚ - Sarah Valin 90°45° 48 ft 5.75 ft 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 x

4. 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 60° - Bailey Gray 60°90° 30° 4.9 ft 12 ft x Trig: tan 60° = x/12 x ≈ 20.78 20.78 ft + 4.9 ft = 25.68 ft

5. 20 ⁰ 60 5.255.25 Cos20 = 60/yCos20(y) = 60y = 60/Cos20y ≈ 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. Y X Braden Pichel1 st 20 ⁰

6. CONCLUSION Angle MeasurementX (height of library arch) 30°26.61 ft 45°53.75 ft 60°25.68 ft 20°27.09 ft AVERAGE33.28 ft 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.