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Trigonometric Height Approximations in Special Triangles

Explore trigonometric approximations to determine the heights in special right triangles. Discover the calculations for 45° and 60° triangles using trigonometry methods. Understand how to find the total height and the height to the eyes in various scenarios.

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Trigonometric Height Approximations in Special Triangles

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  1. How Tall Is It? Jessie Pitts, KelsieSchweer, Julia Zhao, and, Daniel Leatherwood 3rd Period March 8, 2011

  2. Trig approximation- Tan45=x 24 X= 24 Height = 24+ 5.08= 29.08 Special Right Triangle- Leg= Leg 24 ft. = 24 ft. Height= 24 + 5.08 = 29.08 45° Triangle 45° 24 ft. (leg) 29.08 ft.(Total height) 45° 5.08 ft. (Height to eyes.) 24 ft. (Leg)

  3. 30 60° 42 ft 30° Tan30=A/42≈24.25 cos30=42/h≈36.37 90-30=60°

  4. Trig approximation- Tan 60=x 14 X= 24.25 Height = 24.25 + 5.25= 29.08 Special Right Triangle- Short leg= Short leg X √3 Leg Hyp=Short leg X 2 24 ft. = 24 ft. Height= 24 + 5.08 = 29.08 14 x 14√3 ≈ 339.48 Height= 14√3 + 5.25 = 29.50 60 30° 14√3 ft. (long leg) 29.50 ft.(Total height) 60° 5.25 ft. (Height to eyes.) 14 ft. (Short Leg)

  5. 18 Triangle 64ft. 18

  6. Conclusion

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