# Thread: Special Right Trinagle: "...Clay Ave, Rt 35 are straight, perp. to each other."

1. ## Special Right Trinagle: "...Clay Ave, Rt 35 are straight, perp. to each other."

Hello! I understand how to apply the 30-60-90 and 45-45-90 triangle ratios; however, I do not understand how these streets are in relation to each other. A drawing or any help would be appreciated!

"You live on the corner of Clay Ave and Main St. You drive from your apartment due south 9.9 mi on Main St, then due west 13.2 mi on State St to the corner of Clay Ave and Rt 35. You turn left, then head for a store at the intersection of Rt 35 and Main St, then take Main St home from the store. Clay Ave and Rt 35 are straight and perpendicular to one another."

I cannot visualize this. Thanks for your help :)

2. Originally Posted by magn
Hello! I understand how to apply the 30-60-90 and 45-45-90 triangle ratios; however, I do not understand how these streets are in relation to each other. A drawing or any help would be appreciated!

"You live on the corner of Clay Ave and Main St. You drive from your apartment due south 9.9 mi on Main St, then due west 13.2 mi on State St to the corner of Clay Ave and Rt 35. You turn left, then head for a store at the intersection of Rt 35 and Main St, then take Main St home from the store. Clay Ave and Rt 35 are straight and perpendicular to one another."

I cannot visualize this. Thanks for your help
Why not draw one road at a time?

"9.9 m south on Main" -- Okay, then Main is North-South and Clay is East-West. Draw those and indicate your apartment at the intersection.

Next clue?

3. Originally Posted by tkhunny
Why not draw one road at a time?

"9.9 m south on Main" -- Okay, then Main is North-South and Clay is East-West. Draw those and indicate your apartment at the intersection.

Next clue?
Just make sure that only "Clay Ave and Rt 35 are straight and perpendicular to one another." The rest could be curved, slanted, etc.

4. What do you need to find in the problem?

5. Originally Posted by Denis
Lev, so a "corner" (geometry) is not always 90 degrees?
I don't see why we need to assume this. If all streets are straight and all intersections are 90 degrees we get a contradiction:
Main and Rt 35 are normal to Clay, therefore Main and Rt 35 are parallel. And yet there is a "store at the intersection of Rt 35 and Main St".

6. Originally Posted by tkhunny
… then Main is North-South and Clay is East-West …
I don't see how Clay Ave can run East-West. Clay is perpendicular to Rt 35, and Main St intersects both of those roads.

7. I forgot to draw a compass point, but North points up, so West points to the left:

Rt35_&_Clay.jpg

8. Originally Posted by lev888
The [roads other than Clay Ave and Rt 35] could be curved, slanted, etc.
Maybe, but we don't actually have the question-part of the exercise, yet. Answering the question may require an interpretation with straight line-segments only (eg: triangles).

9. Originally Posted by mmm4444bot
I don't see how Clay Ave can run East-West. Clay is perpendicular to Rt 35, and Main St intersects both of those roads.
It's a place to start. If you find inconsistencies in later clues, feel free to revise the model.

10. Originally Posted by tkhunny
It's a place to start.
I see a general model, in the OP: "special triangles, triangle ratios, 30-60-90 and 45-45-90 triangles" (paraphrased).

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