Geometry - triangle problems

stathisgar

New member
Joined
Jun 12, 2019
Messages
1
Hello,

I am a geographer, but never had any serious relation to survey map creation, at least in terms of precision. I was involved in different topics. Although I was good in geometry and mathematics during high-school, years have passed and I am now in a situation that need to have some refresher in basic geometry problems.

My problems started when I had to create a certain triangle with the following length:

side a: 22.5 meters
side b: 23.20 meters
side c: 1.60 meters
height of the triangle from side a to side b: 1.60

No matter how many times I tried, I am not able to create that shape. either side c will be about 1.77 meters, or the height of the triangle will not be 1.60 meters. I am following the measurements of an old shape that was drawed by a surveyor, so before stating that there is a problem related to the old shape measurements I would like to be assured that it is not possible to create such a shape.

Thank you very much for your understanding and help.

PS: I may have some more questions regarding triangles and circles within the next time period.

Best regards,
Stathis
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,561
If the height of the triangle equals the length of a side, then it is a right triangle.

A right triangle must follow the Pythagorean Theorem.

\(\displaystyle \therefore 1.6^2 + 22.5^2 = 2.56 +506.25 = 508.81 \ne 538.24 = 23.2^2.\)

There is no such triangle.
 

LCKurtz

Junior Member
Joined
May 3, 2019
Messages
70
If the height of the triangle equals the length of a side, then it is a right triangle.
That isn't generally true. See:
triangle.jpg
 

lev888

Full Member
Joined
Jan 16, 2018
Messages
282
Area of the triangle given the 3 sides (per wolframalpha.com) is 16.4276
Area of the triangle based on the height 1.6 and side 23.2 (b) is 18.56.
Doesn't work.
 

LCKurtz

Junior Member
Joined
May 3, 2019
Messages
70
You are correct. I forgot all about obtuse triangles. Thank you for the correction.
Although the statement isn't generally true, I think your argument is fine for his problem where he specified the height be measured from "side b" to "side a", where I suppose he meant from angle B, opposite side b, to side a.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
4,125
My problems started when I had to create a certain triangle with the following length:

side a: 22.5 meters
side b: 23.20 meters
side c: 1.60 meters
height of the triangle from side a to side b: 1.60
The basic problem is that you have too much data, and it is inconsistent. Generally, a triangle is determined by 3 facts, and a 4th, if independent, will be typically inconsistent.

Can you tell us where the data came from, and why you thought such a triangle should exist?
 
Top