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Indirect Measurement

Indirect Measurement. By: Audrey Denny, Jon Nuffer , Diana Vivancl , Emily Stevens. Plan. We will try to indirectly measure the pole with our knowledge of right triangles. The first strategy is to use the tangent formula

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Indirect Measurement

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  1. Indirect Measurement By: Audrey Denny, Jon Nuffer, Diana Vivancl, Emily Stevens

  2. Plan • We will try to indirectly measure the pole with our knowledge of right triangles. • The first strategy is to use the tangent formula • Our second strategy is to find a person to measure and use the similar triangle formula • The last strategy is to find the 45 degree angle and then find length with the 45-45-90 formula

  3. Tangent Triangle Strategy First we used the tool below to measure the angle of the shadow to the pole by matching the shadow of our eyes to the tip of the trees shadow. After measuring the angle we measured the length of the pole’s shadow. Now that we had the information we used the tangent button on the angle measure and the length to determine the pole’s length. Tan (41) = x/448; x= Tan (41) (448) Answer: x= 389.4 in.= 32 ft. 5 in. Pole/x 41 degrees 448 in.

  4. Similar Triangle Strategy Pole/x 64 in. Now we found the height of Jon and then his shadow length at the same time that we found the length of the shadow for the pole. Since both triangles are similar we decide to use this fact to find the height of the pole. To find the answer: 64/x = 96/ 448 Final answer:298.6 in. = 24 ft. 10 in. 448 in. 96 in.

  5. 45-45-90 Strategy For the last one we had to look at the top of the pole and measure the angle to exactly 45 degrees using the tool from before. Then we connected the angle to the ground carefully. Afterwards we measured the length of the point in the ground to the bottom of the pole. Since it is at a 45 degree angle it is supposed to mirror the pole. Answer: 407.8 in= 33 ft. 11 in. Pole/x 45 degrees 407.8 in

  6. Comparison • The 45-45-90 strategy is the least accurate because it is hard to exact the 45 degree angle and then measure the length because it may be a few inches off • The tangent strategy is also not the best because when measuring the angle it is approximated because it might have been 41.4 or maybe 42 degrees, we do not know for sure • Lastly the similar triangle method is the obvious choice because it is easiest to measure shadows and heights, so our final answer for the pole is about 24 ft. 10 in.

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