Fernando followed two diagonal paths, Paths 1 and 2, to get from his house, F, to a neighborhood corner store, C, as shown below
.
1 answer:
Answer:
42 meters
Step-by-step explanation:
Given
See attachment for complete question
Required
Calculate distance FC
FC is calculated as:
![FC = Path\ 1 + Path\ 2](https://tex.z-dn.net/?f=FC%20%3D%20Path%5C%201%20%2B%20Path%5C%202)
Where
![Path\ 1 = FB](https://tex.z-dn.net/?f=Path%5C%201%20%3D%20FB)
![Path\ 2 = BC](https://tex.z-dn.net/?f=Path%5C%202%20%3D%20BC)
Considering
, we have:
--- Pythagoras theorem
Where
![FE = FD - BA](https://tex.z-dn.net/?f=FE%20%3D%20FD%20-%20BA)
![FE = 22m - 15m](https://tex.z-dn.net/?f=FE%20%3D%2022m%20-%2015m)
![FE = 7m](https://tex.z-dn.net/?f=FE%20%3D%207m)
and
![BE = CD - CA](https://tex.z-dn.net/?f=BE%20%3D%20CD%20-%20CA)
![BE = 32m - 8m](https://tex.z-dn.net/?f=BE%20%3D%2032m%20-%208m)
![BE = 24m](https://tex.z-dn.net/?f=BE%20%3D%2024m)
So:
![FB^2 = FE^2 + BE^2](https://tex.z-dn.net/?f=FB%5E2%20%3D%20FE%5E2%20%2B%20BE%5E2)
![FB^2 = 7^2 +24^2](https://tex.z-dn.net/?f=FB%5E2%20%3D%207%5E2%20%2B24%5E2)
![FB^2 = 49 +576](https://tex.z-dn.net/?f=FB%5E2%20%3D%2049%20%2B576)
![FB^2 = 625](https://tex.z-dn.net/?f=FB%5E2%20%3D%20625)
Take square roots of both sides
![FB = 25](https://tex.z-dn.net/?f=FB%20%3D%2025)
So:
![Path\ 1 = 25](https://tex.z-dn.net/?f=Path%5C%201%20%3D%2025)
Considering
, we have:
--- Pythagoras theorem
Where:
and ![AC = 8](https://tex.z-dn.net/?f=AC%20%3D%208)
So, we have:
![BC^2 = 15^2 + 8^2](https://tex.z-dn.net/?f=BC%5E2%20%3D%2015%5E2%20%2B%208%5E2)
![BC^2 = 225 + 64](https://tex.z-dn.net/?f=BC%5E2%20%3D%20225%20%2B%2064)
![BC^2 = 289](https://tex.z-dn.net/?f=BC%5E2%20%3D%20289)
Take square roots of both sides
![BC = 17](https://tex.z-dn.net/?f=BC%20%3D%2017)
So;
![Path\ 2= 17](https://tex.z-dn.net/?f=Path%5C%202%3D%2017)
Recall that:
![FC = Path\ 1 + Path\ 2](https://tex.z-dn.net/?f=FC%20%3D%20Path%5C%201%20%2B%20Path%5C%202)
![FC = 25 + 17](https://tex.z-dn.net/?f=FC%20%3D%2025%20%2B%2017)
![FC = 42](https://tex.z-dn.net/?f=FC%20%3D%2042)
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