Pythagorean Theorem on Excel

Target Curriculum: Mathematics

Target Grade: 7 - 9

SOLs: C/T.GR8.1   MAT.8.11  
Time: One class period (55 min)

Objective:
The learner will be able to use Microsoft Excel to
find the length of the third side of a right triangle when given the lengths of the other two sides.

Purpose:
To reinforce the concept of Pythagorean Triples and further students knowledge in the use of spreadsheets.

Materials:
Enough computers for at most two students to a computer.

Procedure:
1. Review mathematical techniques for solving a2 + b2 = c2 for "a," for "b,"
and for "c."

2. Open Microsoft Excel.

A. For students to find "c" when given "a" and "b," do the following:

¨ In cell A1 type: "Finding c when given a & b."
¨ In cell B3 type "a", in cell C3 type "b", and in cell D3 type "c".
¨ In cell A4 type "Triangle 1" and in cell A5 type "Triangle 2."
¨ Now have students find c if a = 3 and b = 4 (this is triangle 1).

1. In cell B4 type the number 3, and in cell C4 type the number 4.
2. Cell D4 requires a formula, so click on "fx".

¨ Under function category highlight "All."
¨ Under function name scroll down to SQRT for square root.
¨ In the number box type: B4*B4 + C4*C4. This will add the squares of a & b and then automatically take the square root of the result.
¨ Click OK and the number 5 should appear in cell D4. So, c = 5.

3. Try finding "c" if a = 5 and b = 12 (triangle 2).

¨ In cell B5 type 5 and in cell C5 type 12.
¨ Go back up to cell D4 and drag down the "dot" in the
Lower right corner to cell D5. This will copy the formula to cell D5 and the number 13 should appear in D5. So c=13.

B. For students to find "b" when given "a" & "c" do the following:

¨ In cell A8 type "Finding b when given a &c."
¨ In cell B10 type "a," in cell C10 type "c," and in cell D10 type "b."
¨ In cell A11 type "Triangle 3" and in cell A12 type "Triangle 4."
¨ Now have students find "b" if a = 9 and c = 41 (triangle 3).

1. In cell B11 type 9 and in cell C11 type 41.
2. Cell D11 requires a formula so click on "fx".

¨ Under function category highlight "All."
¨ Under function name highlight SQRT for square root.
¨ In the number box type C11*C11 - B11* B11. This will subtract the square of b (cell B11) from the square of c (cell C11) and automatically take the square root of the result.
¨ Click OK and the number 40 should appear in cell D11. So, b = 40.

3. Try finding "b" if a = 6 and c = 10.

¨ In cell B 12 type 6 and in cell C12 type 10.
¨ Click on cell D11 and drag the formula down to cell D12. An "8" should appear in cell D12. So, b = 8.

C. For students to find "a" when given "b" and "c" do the following:

¨ In cell A16 type: "Finding a when given b & c."
¨ In cell B18 type "b," in cell C18 type "c," and in cell D18 type "a."
¨ In cell A19 type "Triangle 5" and in cell A20 type "Triangle 6."
¨ Now have students find "a" if b=30 and c=34 (triangle 5).

1. In cell B19 type 30 and in cell C19 type 34.
2. Cell D19 requires a formula so click on "fx".

¨ Under function category highlight "All."
¨ Under function name scroll down to SQRT for square root.
¨ In the number box type: C19*C19 - B19* B19. This will
subtract the square of b (cell B19) from the square of c (cell C19) and automatically take the square root of the result.
¨ Click OK and the number 16 should appear in cell D19. So, a=16.

3. Now have students find "a" if b=21 and c=29 (triangle 6).

¨ In cell B20 type 21 and in cell C20 type 29.
¨ Move to cell D19 and drag the formula down to cell D20.
The number 20 should appear in cell D20. So, a=20.

Observations:
This is not a good activity unless you have at most two students to a computer.

Conclusions:
Students must have motivation to see this through to the end. I, therefore, included a quiz that they must do using Excel. (See attachment 3)

For Your Information:
1. To see a copy of what this looks like on the spreadsheet see attachment 1.
2. For additional exercises see attachment 2.

3. For a student quiz see attachment 3.

Attachment 1

Finding c: given a & b

a b c
triangle 1 3 4 5
triangle 2 5 12 13


Finding b: given a & c

a c b
triangle 3 9 41 40
triangle 4 6 10 8



Finding a: given b & c

b c a
triangle 5 30 34 16
triangle 6 21 29 20

Attachment 2

Additional Exercises

1. Find a if b=35 and c=37.

2. Find b if a= 15 and c=113.

3. Find c if a=16 and b=63.

4. Find a if b=45 and c=53.

5. Find b if a=33 and c=65.

6. Find c if a=39 and b=80.

Answers:

1. 12 2. 112 3. 65 4. 28 5. 56 6. 89

Attachment 3

QUIZ

Find the length of the missing side of each right triangle:

_____1. a=32, b=255, find c.
A. 324 B. 156 C. 19 D. 257

_____2. A=36, c=85, find b.
A. 63 B. 77 C. 103 D. 12

_____3. B=323, c=325, find a.
A. 19 B. 429 C. 36 D. 74

_____4. A=48, b=55, find c.

A. 73 B. 23 C. 59 D. 125

_____5. A=65, c=97, find b.

A. 107 B. 35 C. 72 D. 67

Answers: 1. D 2. B
3. C 4. A
5. C

Extension:
Have students research Pythagorus on the internet and find out some other things that he did or accomplished.

Class Discussion Questions:
1. How does "order of operations" come into play when solving for the missing side of a right triangle?

Cautions and Concerns:
Students have tendencies to rush ahead because they think they know what to do. Things can get messy if they go to far ahead. So try to roam and monitor them - this will save you the time and pain of trying to figure out why their system won't work.