Session 2, Part B: The Role of Ratio

Session 2, Part B:
The Role of Ratio

In This Part: Ratio and Scale | Constant Ratios | Using the Pythagorean Theorem

Remember that the Pythagorean theorem states that in right triangles with leg lengths a and b, and hypotenuse length c, the following relationship holds: a² + b² = c². Note 10 When you use the Pythagorean theorem, your answer may not reduce easily from radical form (as a square root). Rather than using a calculator to take the square root, you can instead express the answer in reduced radical form. Here's how: Express the number as a product of factors, where one of the factors (if possible) is a square number. Then take the square root of just the square number and leave the answer as a product of the square root and the radical:

Problem B8

a.
Use the Pythagorean theorem to find the lengths of the hypotenuses for all the triangles from Problem B6. Leaving the length in radical form, fill in the blank columns in the chart below. Do this on paper by printing this page if it's not possible to type in the square root symbol on your computer. Notice the patterns in the ratio of H:S.

Side Lengths (S) in cm

Hypotenuse Length (H) in cm

Ratio S:S

Pythagorean Ratio H:S

1

1:1

2

2:2

3

3:3

4

4:4

5

5:5

6

6:6

Here is the completed table:

Side Lengths (S) in cm

Hypotenuse Length (H) in cm

Ratio S:S

Pythagorean Ratio H:S

1

1:1

:1

2

2

2:2

2:2

3

3

3:3

3:3

4

4

4:4

4:4

5

5

5:5

5:5

6

6

6:6

6:6

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b.
Which measures are more accurate -- those done with a ruler or those determined using the Pythagorean theorem? Explain.


Problem B9
In most right triangles, one or more of the side-length values is irrational. Note 11 In terms of measurement, what are the implications of one or more of the values being irrational?

Next > Part C: Precision and Accuracy

Session 2: Index | Notes | Solutions | Video