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

#### magn

##### New member
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

#### tkhunny

##### Moderator
Staff member
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?

#### lev888

##### Full Member
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.

#### lev888

##### Full Member
What do you need to find in the problem?

#### lev888

##### Full Member
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".

#### mmm4444bot

##### Super Moderator
Staff member
… 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.

#### mmm4444bot

##### Super Moderator
Staff member
I forgot to draw a compass point, but North points up, so West points to the left:

#### mmm4444bot

##### Super Moderator
Staff member
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).

#### tkhunny

##### Moderator
Staff member
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.

#### mmm4444bot

##### Super Moderator
Staff member
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).

#### tkhunny

##### Moderator
Staff member
I see a general model, in the OP: "special triangles, triangle ratios, 30-60-90 and 45-45-90 triangles" (paraphrased).
No objection.

#### mmm4444bot

##### Super Moderator
Staff member
… you belong in the Mapping Business!
No, thanks. Other interpretations are possible; I'm hoping there's more to the exercise than just submitting one of them (else, I gave away an answer).