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Calculating Goal Post Height Using Trigonometry and Geometry Techniques

This project explores the application of trigonometry and geometry to calculate the height of a goal post. By using tangent functions for angles of 30°, 45°, and 60°, we derive various lengths in relation to a person's height. For instance, we find the heights corresponding to different angles and legs of triangles. The average calculated goal post height is approximately 27.62 feet. This demonstrates how mathematical principles can aid in real-world applications in architecture and design.

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Calculating Goal Post Height Using Trigonometry and Geometry Techniques

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  1. How Tall Is It?2011 Maddie Wohlfarth Will Freeman Maryellen Newton Madeline Held

  2. 30° Tan=opp/adj Tan30=x/40 Tan30*40=x x≈23.09 x 30° 40 Short leg= long leg / √3 40/√3=x 23.09=x x + my height ( up to my eyes) = the height of the goal post 23.09+5=height of goal post • Goal post= 28.09 feet

  3. 45° 45° x ft Tan=opp/adj Tan45=x/22 Tan45(22)=x x=22 ft 45° 90° 22 ft In a 45-45-90 Δ, leg=leg, so x=22 ft. My height to my eyes≈5.58 ft Height of the Goalpost≈27.58 ft 22 ft+5.58 ft=27.58 ft

  4. 60° xft x+my height ( up to my eyes)=the height of the goal post 24.25+4.8=height of goal post Goal post=29.05 Tan=opp/adj Tan60=x/14 Tan60*14=x x=24.25 60° Short leg=Long leg√3 14=x√3 x=14/√3 x=24.25 14 ft

  5. x + my height ( up to my eyes) = the height of the goal post 20.52+5.25=height of goal post Goal post=25.77 25° Tan 25= Tan 25= x x≈20.52 25° 44 ft.

  6. Conclusion We learned how to use geometry, trigonometry, and special right Δs in everyday life to solve for height and length based problems that can be used in architecture and design. Our average goal post height was 27.62.

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