Question

maurice brewer-myers - 8.6c mystery pixel art: pythagorean theorem
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f10:f11
questions
#
answer
directions: calculate
1
1
6
2
8
1
10
2
2
12
9
2
15
3
3
8
4
15
3
17
4
4
5
3
4
5
5
7.1
6
11.5
5
6
2.7
5.7
6
7
12
8
16
7
20
8
5
12
8
13
9
10
26
10
18
9
24
10
30
sheet1

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\) (if \(c\) is the hypotenuse) or for finding a leg, \(a^{2}=c^{2}-b^{2}\).

Step2: Solve for the missing side of the first triangle in row 2

Given \(a = 6\) and \(b = 8\), then \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Step3: Solve for the missing side of the second triangle in row 2

Given \(a = 9\) and \(c = 15\), then \(b=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144}=12\).

Step4: Solve for the missing side of the first triangle in row 3

Given \(a = 8\) and \(b = 15\), then \(c=\sqrt{8^{2}+15^{2}}=\sqrt{64+225}=\sqrt{289}=17\).

Step5: Solve for the missing side of the second triangle in row 3

Given \(a = 3\) and \(c = 5\), then \(b=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\).

Step6: Solve for the missing side of the first triangle in row 4

Given \(a = 7.1\) and \(b = 11.5\), then \(c=\sqrt{7.1^{2}+11.5^{2}}=\sqrt{50.41+132.25}=\sqrt{182.66}\approx13.52\) (seems there is an error in the problem - setup as the expected answer is likely based on integer - like Pythagorean triples in the context).

Step7: Solve for the missing side of the second triangle in row 4

Given \(a = 2.7\) and \(b = 5.7\), then \(c=\sqrt{2.7^{2}+5.7^{2}}=\sqrt{7.29 + 32.49}=\sqrt{39.78}\approx6.31\) (again, likely an error in the problem - setup).

Step8: Solve for the missing side of the first triangle in row 5

Given \(a = 12\) and \(b = 16\), then \(c=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20\).

Step9: Solve for the missing side of the second triangle in row 5

Given \(a = 5\) and \(b = 12\), then \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25+144}=\sqrt{169}=13\).

Step10: Solve for the missing side of the first triangle in row 6

Given \(a = 10\) and \(c = 26\), then \(b=\sqrt{26^{2}-10^{2}}=\sqrt{676 - 100}=\sqrt{576}=24\).

Step11: Solve for the missing side of the second triangle in row 6

Given \(a = 18\) and \(c = 30\), then \(b=\sqrt{30^{2}-18^{2}}=\sqrt{900 - 324}=\sqrt{576}=24\).

Answer:

The answers for the missing sides of the right - triangles (in the order of the table) are: 10, 15, 17, 4, (unclear values as per the above - mentioned issues), 20, 13, 24, 30.