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Indirect Measurement

Indirect Measurement. By: Zachary Bonney, Ty Pena, Kelly Mckenna, and Mariah Lukenbill P.3. The indirect measurement of a tree!. There are three methods that we will use to find the height of the tree. Similar Triangles Trigonometry 30-60-90. Similar Triangles.

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Indirect Measurement

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  1. Indirect Measurement By: Zachary Bonney, Ty Pena, Kelly Mckenna, and Mariah Lukenbill P.3

  2. The indirect measurement of a tree! There are three methods that we will use to find the height of the tree. • Similar Triangles • Trigonometry • 30-60-90

  3. Similar Triangles X 123 in. 404 in. 75

  4. Theorems/equations and Data We used the geometric mean theorem. The missing height(X) was put over the total length, 404 and set equal to 75 over 123. Total length: 404 in Height of tree: X Ty’s height: 75 in Length from Ty to base of shadow: 123 in.

  5. Calculations for Similar Triangles

  6. Trigonometry X Tan(?) = opp 31 404 in. adj.

  7. Equation/Theorem used and Data We used Example 3 of 7.5, to estimate the height using Tangent. Data: Degrees used: 31 Total length(Adjacent):404 in. Height of tree(Opposite): X Tan(?) =

  8. Calculations for Trigonometry

  9. 30-60-90 X 90 60 145 in.

  10. Equations used/Data We used theorem 7.9 which states in a 30/60/90 triangle; the hypotenuse is twice as long as he shorter leg. While the longer leg is times as long as the shorter leg. Data: short leg: 145 in. Longer leg: short leg times

  11. Calculations for 30-60-90

  12. Comparison/Analysis. Overall all three of our results seem to be very well in the ballpark. Each one appeared to be fairly close to each other.Using trigonometry yielded a height of 20.23 ft.Similar Triangles produced a value of 20.53 ft. Finally the 30/60/90 produced the tallest tree at 20.93 ft. Trigonometry: 20.23 ft Similar triangles: 20.53 ft 30/60/90: 20.93 ft. Each result was in the range of each other by .3 ft or .4 ft off. We believe that trigonometry produced the most accurate results, as it could almost be the median of the three heights. Similar seemed to be the hardest, as you needed something to form a second right triangle so there were more lengths that could be off. According to trigonometry, as long as you are able to find the acute angle, you can always find the length of the second leg. That is why, we believe trig, to be the best option.

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