To measure the distance (DC) across a pond, a surveyor takes points A and B so that AB is parallel to DC. If AB = 60 feet, EB = 48 feel, and ED = 80 feet, find DC.

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- Jan 15th 2007, 07:51 PMsymmetryFind DC
To measure the distance (DC) across a pond, a surveyor takes points A and B so that AB is parallel to DC. If AB = 60 feet, EB = 48 feel, and ED = 80 feet, find DC.

- Jan 16th 2007, 04:45 AMCaptainBlack
- Jan 16th 2007, 09:42 AMSoroban
Hello, symmetry!

Quote:

To measure the distance $\displaystyle DC$ across a pond,

a surveyor takes points $\displaystyle A$ and $\displaystyle B$ so that $\displaystyle AB \parallel DC$.

If $\displaystyle AB = 60\text{ ft},\;EB = 48\text{ ft},\;ED = 80\text{ ft}$, find $\displaystyle DC$.

Code:`D * - - - - - - - - - - - - - - - * C`

* *

80 * *

* *

*E

* * 48

* *

A * - - - - - - - - - - - * B

60

From the similar triangles, we have: .$\displaystyle \frac{CD}{80} \:=\:\frac{60}{48}$

Therefore: .$\displaystyle CD \:=\:100\text{ ft}$

- Jan 16th 2007, 10:05 AMgalactus
In real-life, the person helping the surveyor would go to the other side of the pond with a prism and the surveyor would measure the distance with the transit. That's no fun, though. Too easy.

- Jan 16th 2007, 01:21 PMsymmetryok
Thank you all, especially soroban. Soroban did a great job with the picture and reply.

Thanks!