HOW TALL IS IT?

By: Kenneth Casey, Braden Pichel, Sarah Valin, Bailey Gray

1st Period – March 8, 2011

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 trianglesLong leg= short leg √336=x√3(36/√3) = (x√3/√3)X=(36/√3) (√3/√3)X=36√3/3X=12√3=20.78ft.20.78 ft + 5.83 ft = 26.61 ft.

Kenneth Casey 1st

45˚ - Sarah Valin

90°45°

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

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 ft12 ft

x

Trig: tan 60° = x/12 x ≈ 20.78

20.78 ft + 4.9 ft = 25.68 ft

20⁰ 605.25 5.25

Cos20 = 60/y Cos20(y) = 60 y = 60/Cos20 y ≈ 63.85 ft.

Tan20 = x/60 x = Tan20(60) x ≈ 21.84 ft.

Height = x + 5.25 Height = 21.84 + 5.25 Height ≈ 27.09 ft.

YX

Braden Pichel 1st 20⁰

CONCLUSION

Angle Measurement X (height of library arch)

30° 26.61 ft

45° 53.75 ft

60° 25.68 ft

20° 27.09 ft

AVERAGE 33.28 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.