Question

part 2: given that each unit on the coordinate grid is 100 feet, answer the following questions. round your answer to the tenths place. (remember means that after solving the pythagorean theorem for each distance, you need to multiply your answer by 100.)

1. walt disney railroad to winnie the pooh adventure $10^{2}+3^{2}=c^{2}$
2. tom sawyer island to the hall of presidents $1^{2}+2^{2}=c^{2}$
3. buzz lightyears spa spin to mad tea party $1^{2}+6^{2}=c^{2}$
4. jungle cruise to the barnstormer $6^{2}+13^{2}=c^{2}$
5. peter pans flight to astro orbiter $3^{2}+11^{2}=c^{2}$
6. legend of the lion king indy speedway $1^{2}+7^{2}=c^{2}$
7. the timekeeper to big thunder mountain railroad $5^{2}+13^{2}=c^{2}$
8. the enchanted tiki room to the haunted mansion $2^{2}+5^{2}=c^{2}$
9. the alien encounter to splash mountain $2^{2}+14^{2}=c^{2}$
10. juan and michael are supposed to walk from small world. michael has to walk further? by $4^{2}+11^{2}=c^{2}$

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the other two sides. After finding \(c\), we multiply by 100.

Step2: Solve for each case

Case 1: \(a = 10\), \(b = 3\)

First, calculate \(c=\sqrt{10^{2}+3^{2}}=\sqrt{100 + 9}=\sqrt{109}\approx10.44\). Then multiply by 100: \(10.44\times100 = 1044.0\)

Case 2: \(a = 1\), \(b = 2\)

Calculate \(c=\sqrt{1^{2}+2^{2}}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\). Multiply by 100: \(2.24\times100=224.0\)

Case 3: \(a = 1\), \(b = 6\)

Calculate \(c=\sqrt{1^{2}+6^{2}}=\sqrt{1+36}=\sqrt{37}\approx6.08\). Multiply by 100: \(6.08\times100 = 608.0\)

Case 4: \(a = 6\), \(b = 13\)

Calculate \(c=\sqrt{6^{2}+13^{2}}=\sqrt{36 + 169}=\sqrt{205}\approx14.32\). Multiply by 100: \(14.32\times100=1432.0\)

Case 5: \(a = 3\), \(b = 1\)

Calculate \(c=\sqrt{3^{2}+1^{2}}=\sqrt{9 + 1}=\sqrt{10}\approx3.16\). Multiply by 100: \(3.16\times100=316.0\)

Case 6: \(a = 1\), \(b = 7\)

Calculate \(c=\sqrt{1^{2}+7^{2}}=\sqrt{1 + 49}=\sqrt{50}\approx7.07\). Multiply by 100: \(7.07\times100=707.0\)

Case 7: \(a = 5\), \(b = 13\)

Calculate \(c=\sqrt{5^{2}+13^{2}}=\sqrt{25+169}=\sqrt{194}\approx13.93\). Multiply by 100: \(13.93\times100 = 1393.0\)

Case 8: \(a = 2\), \(b = 5\)

Calculate \(c=\sqrt{2^{2}+5^{2}}=\sqrt{4 + 25}=\sqrt{29}\approx5.39\). Multiply by 100: \(5.39\times100=539.0\)

Case 9: \(a = 2\), \(b = 4\)

Calculate \(c=\sqrt{2^{2}+4^{2}}=\sqrt{4 + 16}=\sqrt{20}\approx4.47\). Multiply by 100: \(4.47\times100=447.0\)

Case 10: \(a = 4\), \(b = 11\)

Calculate \(c=\sqrt{4^{2}+11^{2}}=\sqrt{16 + 121}=\sqrt{137}\approx11.70\). Multiply by 100: \(11.70\times100=1170.0\)

Answer:

1. \(1044.0\)
2. \(224.0\)
3. \(608.0\)
4. \(1432.0\)
5. \(316.0\)
6. \(707.0\)
7. \(1393.0\)
8. \(539.0\)
9. \(447.0\)
10. \(1170.0\)