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Indirect Measurement group project

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Indirect Measurement group project

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

- TANGENT
- TRIANGLE SIMILARITY THM
- 30-60-90 TRIANGLE THM

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

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 • 88Cross multiply

26474 = 88xDivided by 88

300.841 ≈ x

- 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 • √330-60-90 ∆ Triangle thm

35.5 = y√3substitute

35.5 = ydivide each side by 3

√3

35.5 • √3 = yMultiply numerator and denominator by √3

√3 √3

35.5√3 = yMultiply fractions

3

y ≈ 20.496 ft.Use calculator to approximate answer

y

x

20.296 + 3.6 ft = xAdd the eye height to the total distance

23.896 ft = xadd to find height

Eye height

- 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.