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How Tall Is It?. By: Nikolas Kassouf, Angelo Drakos , David Sessamen , and Ben Claude. 30 Degree angle . Special Right Triangles sh. leg = sh. leg/ √3 sh. leg = 42 /√3 sh. leg = 14√3 Hyp = sh. leg × 2 Hyp = 14√3 × 2 Hyp = 28√3ft. Trigonometry (Hyp) cos30 = 42/hyp

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slide1

How Tall Is It?

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

slide2

30 Degree angle

Special Right Triangles

sh. leg = sh. leg/ √3

sh. leg = 42 /√3

sh. leg = 14√3

Hyp = sh. leg × 2

Hyp = 14√3 × 2

Hyp = 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

4.83ft.

42ft.

Special Right + 4.83ft. = 18.83 √3 ft.

Trigonometry + 4.83ft. ≈ 29.08 ft.

slide3

Special Right Triangles

Leg = leg

26 = 26

Hyp = sh. Leg * √2

Hyp = 26 × √2

Hyp = 26√2

45 Degree angle

Special Right + 4.83 = 30.83ft.

Trigonometry + 4.83 ≈ 30.83ft.

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

4.83 ft.

26 ft.

slide4

60 Degree Angle

Special Right + 5.3 = 19.3√3ft.

Trigonometry + 5.3 ≈ 29.55ft.

Special Right Triangles

Hyp = sh. leg × 2

Hyp = 14 × 2

Hyp = 28ft.

L. leg = sh. Leg * √3

L. leg = 14 × √3

L. 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

5.3ft.

14ft.

slide5

20 Degree Angle

5.5ft.

56ft.

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

slide6

The Conclusion

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 three

2) 45 degrees – since leg = leg, the side was the same as the side given

3) 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.