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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

Indirect Measurement group project

By: Group #2 - Taylor Gowan, Olivia Strandin, AryannaGorospe and Angelo Commandatore


Strategies
Strategies

  • TANGENT

  • TRIANGLE SIMILARITY THM

  • 30-60-90 TRIANGLE THM


Tangent
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


Triangle similarity
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


30 60 90 triangle thm
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


30 60 90 triangle thm continued
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


Comparison
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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