Question 1114
<font face = "courier new" size = 2>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"?
`<b>
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 <font color = "red">red</font> below:
`                              
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` D
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |15 north
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `8east|
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |ŻŻŻŻŻ<font color = "red">|</font>
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |9 ` `<font color = "red">|9 north</font>
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |north<font color = "red">|</font>
` ` ` ` ` ` ` ` ` ` `H----------<font color = "red">-------</font>
` ` ` ` ` ` ` ` ` ` ` ` 10 east `<font color = "red">8east</font>
`
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 = 9<u>00   </u>
` ` ` c = <font face = "symbol">Ö</font>900 = 30 miles 
`
Edwin