# Geometry - triangle problems

#### stathisgar

##### New member
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
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
If the height of the triangle equals the length of a side, then it is a right triangle.
That isn't generally true. See:

#### lev888

##### Full Member
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
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
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?