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Indirect Measurement Project

Indirect Measurement Project. By Matt Dun, Kelsey Tremewan, Luis Aguilar, and Sara Shirakh. Methods for measuring the height of the flagpole: Trigonometry Similar Triangles 45-45-90 Triangles. Trigonometry: We measured 50ft. out from the base of the flag pole.

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Indirect Measurement Project

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  1. Indirect Measurement Project By Matt Dun, Kelsey Tremewan, Luis Aguilar, and Sara Shirakh

  2. Methods for measuring the height of the flagpole: • Trigonometry • Similar Triangles • 45-45-90 Triangles

  3. Trigonometry: • We measured 50ft. out from the base of the flag pole. • Then we measured Luis’ eye level which was 5ft. off the ground. • Then we found the angle of elevation with an inclinometer by having Luis stand at the 50 foot mark and looking up to the top of the flag pole. The angle of elevation was 40 degrees. • We use this information to make an equation which was: Tan(40)=h/50 • Then we solved the equation and for the height of the flag pole, we got about 42ft. • We then added 5ft.(Distance from ground to Luis’ eye level) to the 42ft. to get a total height of 47ft.

  4. Trigonometry 42 feet 40 degrees 50 feet 5 feet 5 feet

  5. Similar Triangles: • First we measured the length of the flag pole’s shadow, which was: 86ft. • Then Kelsey stood beside the shadow to match both ends of her shadow and the flag pole’s shadow. • After that we measured the length of Kelsey’s’ shadow which was 8ft. 6in. • Then we also measured the height of Kelsey to the top of her head, which was: 5ft. 5in. • After we had all our measurements we needed, we made them all into inches. • Finally we made a ratio: 65/h=102/1032 • With this method the height of the flagpole is about 55ft.

  6. Similar Triangles 5ft 5in 8ft 6in 86 feet

  7. 45-45-90 Triangle: • With the inclinometer aimed at the top of the flagpole Luis stepped back from the base of the flagpole until the inclinometer read 45 degrees which was at 48ft. • Then we used our knowledge of 45-45-90 triangles to figure out that the length of the other leg is also 48ft. because 45-45-90 triangles legs are congruent.

  8. 45-45-90 triangle 45 degrees 45 degrees 90 degrees 5ft 5ft 48ft

  9. Comparison: Trigonometry:47ft. Similar Triangles:55ft. 45-45-90 Triangle:48ft. Our results were all fairly close except when using similar triangles. We think that trigonometry and 45-45-90 triangles got us more accurate results because they were each only one foot from the other (47&48 feet). With the use of the inclinometer we believe we were fairly accurate in our results for trig and 45-45-90 triangle. We think that the use of similar triangles was less accurate than the 2 other methods we used.

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