Question

map of magic kingdom
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: this means that after solving the pythagorean theorem for each distance, you will need to multiply your answer by 100.)

1. walt disney railroad to winnie the pooh adventure (10^{2}+5^{2}=c^{2}) 1044.0
2. tom sawyer island to the hall of presidents (1^{2}+2^{2}=c^{2}) 224.0
3. buzz lightyears space spin to mad tea party (1^{2}+6^{2}=c^{2}) 608.0
4. jungle cruise to the barnstormer (6^{2}+13^{2}=c^{2}) 1452.0
5. peter pans flight to astro orbiter (3^{2}+11^{2}=c^{2}) 916.0
6. legend of the lion king to indy speedway (1^{2}+7^{2}=c^{2}) 707.0
7. the timekeeper to big thunder mountain railroad (5^{2}+13^{2}=c^{2}) 1393.0
8. the enchanted tiki room to the haunted mansion (2^{2}+5^{2}=c^{2}) (c = 539.6)
9. the alien encounter to splash mountain (2^{2}+14^{2}=c^{2})
10. juan and michael are supposed to meet at space mountain. juan has to walk from small world. michael has to walk from country bear jamboree. who has to walk further? by how much. (4^{2}+11^{2}=c^{2}) (1^{2}+15^{2}=c^{2}) 447.0

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the lengths of the two - legs of a right - triangle and $c$ is the length of the hypotenuse. In the context of the coordinate grid, the horizontal and vertical distances between two points form the legs of a right - triangle, and the straight - line distance between them is the hypotenuse. After finding $c$, we multiply by 100 to get the distance in feet.

Step2: Solve for Juan's distance

For Juan, if $a = 4$ and $b = 11$, then $c_{1}=\sqrt{4^{2}+11^{2}}=\sqrt{16 + 121}=\sqrt{137}\approx11.7$. Multiply by 100: $11.7\times100 = 1170$ feet.

Step3: Solve for Michael's distance

For Michael, if $a = 1$ and $b = 15$, then $c_{2}=\sqrt{1^{2}+15^{2}}=\sqrt{1+225}=\sqrt{226}\approx15.0$. Multiply by 100: $15.0\times100 = 1500$ feet.

Step4: Find the difference

The difference in their distances is $1500 - 1170=330$ feet.

Answer:

Michael has to walk further. By 330 feet.