SOLUTION: The Garcias left home and drove 10 miles east, 9 miles north, 8 miles east, and 15 miles north. How many miles were the Garcias from their home "as the crow flies"?

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Question 1114: The Garcias left home and drove 10 miles east, 9 miles north, 8 miles east, and 15 miles north. How many miles were the Garcias from their home "as the crow flies"?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The Garcias left home and drove 10 miles east, 9 miles north, 8 miles east,
and 15 miles north. How many miles were the garcias from their home "as the
crow flies"?
`
See the diagram below. H represents "home", and D represents the
destination. "Right" is east, "up" is north. "Ignore the tic-marks " ` ".
(They are necessary since the formatting is so limited on here.)
`
`
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` D
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |15 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `8east|
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |ŻŻŻŻŻŻ
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |9 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` `H----------
` ` ` ` ` ` ` ` ` ` ` ` 10 east
`
Extend the lines as show in red below:
`
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` D
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |15 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `8east|
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |ŻŻŻŻŻ|
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |9 ` `|9 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |north|
` ` ` ` ` ` ` ` ` ` `H-----------------
` ` ` ` ` ` ` ` ` ` ` ` 10 east `8east
`
Now all you have is this right triangle:
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` D
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` / |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` / ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` |24 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` / ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` `H-----------------
` ` ` ` ` ` ` ` ` ` ` ` ` ` 18 east
`
Use the Pythagorean theorem
`
HD = c, a = 18, b = 23
`
` ` `c² = a² + b²
` ` `c² = 18² + 24²
` ` `c² = 900
` ` ` c = Ö900 = 30 miles
`
Edwin