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Indirect Measurement

Indirect Measurement. By: Jessop, Zach, John, Trentin. Situation. We are trying to find the height of the basketball rim in the big gym. We found that the distance from the ground to the free

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Indirect Measurement

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  1. Indirect Measurement By: Jessop, Zach, John, Trentin

  2. Situation We are trying to find the height of the basketball rim in the big gym. We found that the distance from the ground to the free throw line is 15 feet. Angle of elevation from Zach’s eye level was 35 degrees. The distance from the ground to Zach’s eye level is 2.5 feet. What is the height of the rim in the gym?

  3. Tan(35)=X/15 X=Tan(35)x15 X is approx 10.5ft

  4. MATHEMATICAL STRATEGY#1 Since we knew the distance from the ground to the free throw line as 15 feet (long leg) and we also knew the angle of elevation as 35 degrees we decided to use Tangent as our first method to determine the height of the rim. Our result was that the rim is approx. 10.5 feet above the ground.

  5. Mathematical Strategy #2 John is 6ft 1in. 6’1”-2’5” is 3’8”. That is one side of the small triangle. The long leg is 6’8” because that is how far John is standing from Zach at the free throw. The proportion is X/3’8”=15’/6’8”+2’5”=10.7ft.

  6. Mathematical strategy #3 Angle C is 30 in both triangles. Angle B is 90 in both triangles. (Big and Small) So they are similar by AA similarity.

  7. Comparing the strategies Tan and the proportion strategy came out with very similar answers. We feel if done right tan is the most accurate way to measure the height of an unknown side. Triangle similarity was the least accurate but very easy and useful if you want a quick answer.

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