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Indirect Measurement group project

Indirect Measurement group project. By: Group #2 - Taylor Gowan, Olivia Strandin , Aryanna Gorospe and Angelo Commandatore. Strategies. TANGENT TRIANGLE SIMILARITY THM 30-60-90 TRIANGLE THM. TANGENT. Tangent = opposite adjacent Tan 32 = Y

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Indirect Measurement group project

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  1. Indirect Measurement group project By: Group #2 - Taylor Gowan, Olivia Strandin, AryannaGorospe and Angelo Commandatore

  2. Strategies • TANGENT • TRIANGLE SIMILARITY THM • 30-60-90 TRIANGLE THM

  3. TANGENT Tangent = opposite adjacent Tan 32 = Y 427 0.624869 = Y 427 Y= 266.819in + 58 324.819in = x Step 1. Draw picture of your triangle Step 2. Add information and measurements Step 3. Tangent definition Step 4. plug in measurements Step 5. Use calculator for Tan 32 Step 6. Multiply by 427 Step 7. add in eye height

  4. Triangle Similarity Height of person = Height of Pole length of persons shadow shadow of pole ∆ similarity thm 62in = x inPlug in #s 88in 427in 62 • 427 = x • 88 Cross multiply 26474 = 88x Divided by 88 300.841 ≈ x

  5. 30-60-90 TRIANGLE THM • In a 30-60-90 ∆, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg. y 35.5 ft Longer leg = shorter leg • √3 30-60-90 ∆ Triangle thm 35.5 = y√3 substitute 35.5 = y divide each side by 3 √3 35.5 • √3 = y Multiply numerator and denominator by √3 √3 √3 35.5√3 = y Multiply fractions 3 y ≈ 20.496 ft. Use calculator to approximate answer

  6. 30-60-90 Triangle THM continued… y x 20.296 + 3.6 ft = x Add the eye height to the total distance 23.896 ft = x add to find height Eye height

  7. Comparison • Triangle similarity = 300.841in and 25.0701ft • Tangent = 324.819in and 27.06825 ft • 30-60-90 Triangle thm= 286.752in and 23.896 ft The Triangle similarity theorem seemed to be best because its simpler to find the measurement of a shadow then an angle. The numbers seemed to be fairly close to each other. Around the 20s. The most accurate strategy was the 30-60-90 Triangle thm because this gave us the exact angle measure. (30º) with the other two strategies we had to estimate the angle measure. I would recommend the Triangle similarity theorem for others to try. It was the most efficient in time and least amount of work.

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