How Tall Is It?

By: Nikolas Kassouf, Angelo Drakos, David Sessamen, and Ben Claude

42ft.4.83ft.

Special Right Trianglessh. leg = sh. leg/ √3sh. leg = 42 /√3sh. leg = 14√3 Hyp = sh. leg × 2Hyp = 14√3 × 2Hyp = 28√3ft.

Trigonometry(Hyp) cos30 = 42/hyp 42/cos30 = hyp hyp ≈ 48.90(Sh. leg) tan30 = Sh. leg/ 42 tan30 × 42 = Sh. leg Sh. leg ≈ 24.25

Special Right + 4.83ft. = 18.83 √3 ft.Trigonometry + 4.83ft. ≈ 29.08 ft.

26 ft.4.83 ft.

Special Right TrianglesLeg = leg26 = 26Hyp = sh. Leg * √2Hyp = 26 × √2Hyp = 26√2

Trigonometry(Hyp) cos45 = 26/hyp 26/cos45 = hyp hyp ≈ 36.78(L. leg) tan45 = L. leg/ 26 tan45 × 26 = L. leg L. leg ≈ 26.00

Special Right + 4.83 = 30.83ft.Trigonometry + 4.83 ≈ 30.83ft.

14ft.5.3ft.

Special Right TrianglesHyp = sh. leg × 2Hyp = 14 × 2Hyp = 28ft.L. leg = sh. Leg * √3L. leg = 14 × √3L. leg = 14√3

Trigonometry(Hyp) cos60 = 14/hyp 14/cos60 = hyp hyp ≈ 28.00(L. leg) tan60 = L. leg/ 14 tan60 × 14 = L. leg L. leg ≈ 24.25

Special Right + 5.3 = 19.3√3ft.Trigonometry + 5.3 ≈ 29.55ft.

56ft.5.5ft.

Trigonometry(Hyp) cos20 = 56/hyp 56/cos20 = hyp hyp ≈ 59.59(Sh. leg) tan20 = Sh. leg/ 56 tan20 × 56 = Sh. leg L. leg ≈ 20.38

Trigonometry + 5.5ft. = 25.88

The average of the height of the wall using Special Right Triangles ≈ 32.29 The average of the height of the wall using Trigonometry ≈ 28.84

The way that we calculated the side of the wall was by using either Special Right Triangles or Trigonometry. In Special Right we either did the following procedures:

1) 30 degrees – divided the long leg by the square root of three2) 45 degrees – since leg = leg, the side was the same as the side given3) 60 degrees – multiplied the long leg by the side given and √3

For Trigonometry, we did the following operations:1) 30 degrees – multiplied the tangent of 30 and the side given, 42 ft.2) 45 degrees – multiplied the tangent of 45 and the side given, 26 ft.3) 60 degrees – multiplied the tangent of 60 and the side given, 14 ft.4) 20 degrees – multiplied the tangent of 20 and the side given, 56 ft.

For all operations, we had to add our height of ourselves to our eyes to get the total height of the wall.