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Height Measurement Techniques Using Trigonometry

Explore effective methods of determining object heights using trigonometry and special right triangles. Discover insights on angle measurements and spatial relationships when calculating height. Average height approximation is around 26.45 ft.

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Height Measurement Techniques Using Trigonometry

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  1. How Tall Is It? an Alec Hudson, Gabi Vargas, Alexis Smith, and Kay Yoshida Production 5th Period 2-25-11

  2. Alec Hudson 12 Cos 30= _________ x 12 X= ________ = 24 Cos 30 Sin x= _________ = 60 12 13.86 60º Sin 30= _______ x 12 18 Ft 24 Ft X= Sin 30* 12= 18 90º In a 30, 60, 90 triangle… 30º Sh. Leg= 12 L Leg= 12 √3 Hyp= 24 12 FT 5 Ft The wall’s height is =18+5 =23 ft.

  3. Gabriela Vargas Trigonometry Tan 45 =Opp Leg 18 Opp leg=18 Cos 45= 18 Hypo Hypo = 25.46 45° Special Right Triangles 45-45-90 25.46 Ft 18 Ft Hypo =√2 leg Hypo = √2 18 Hypo= 18√2 Leg = leg 18 = 18 90° 45° 4’9 Ft 18 Ft The wall’s height = Long leg + my height 18 + 4.08 =22.08 ft.

  4. Alexis smith • Tan 50 = x • 20 • X= 23.84 • Sin 40 = 20 • x • X= 31.11 • The wall’s height: • 23.84 + 5’1’’ = 28.92 ft. 40° 31.11 ft. 23.84 ft. 50 ° ° 90° 20 ft. 5’1” ft.

  5. Trigonometry Kay yoshida Tan30=X/47 X≈27.14 Cos30=47/X X≈54.27 Special Right Triangle 54.27ft. Since it’s a 30, 60, 90 triangle… 60° Short leg= 47√(3) 27.17ft. 3 30° Long leg=47ft 4’8” ft. Hyp=SL*2= 9√(3) 47ft. 3 The wall’s height… =27.14ft.+4’8” =27.14+4 8/12 =27.14+4.67 ≈ 31.81

  6. Conclusion • We learned that you can find the height of an object by either using trigonometry and/or special right triangles. • As the angle measurement got bigger, the more space between the person and the wall. • As the angle measurement got smaller, the less space between the person and the wall. • The bigger the angle, the bigger the triangle. • Average height≈26.45

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