MHB Contradictory Scalene Obtuse Tn Heights

[Kruidnootje]

I plotted 3 points on Google Earth.
West (point A) to slightly North point (point B)= 1284 Km A-B
From Point B to further East Point (point C) = 1717 Km
Then a straight direct line from point C back to point A

The Perimeter = 6001 Km
Area = 57 491 Km

Angle A = 1.711 degrees
Angle B = 177.01 degrees
Angle C = 1.279 degrees
(sorry can't find any degree sign symbol on the right)

Problem:
When I drop a perpendicular line down from Angle B to the longest line (3000) the height is 18 Km
When I calculate by using the formula h = 57491/1500 = 38.33 Km

Is the discrepancy caused by the curvature of the Earth on Google maps? Can one even form an accurate triangular representation in this manner?

 

[HOI]

If you were working on a flat plane then you would have a right triangle with legs of length 1284 and 1717 km. The third side, the hypotenuse would have length $\sqrt{(1284)^2+ (1717)^2}= 2144$ km so the perimeter would be $1284+ 1717+ 2144= 5145$ km, not the "6000" km you have.

Since this is already a right triangle, I don't know why you construct another altitude. The area is just (1/2)(1284)(1717)= 1102314 square kilometers.

(And the area is in square kilometers, not kilometers.)

 

[Kruidnootje]

View attachment 8035

Hallo countryboy
As you can see from the actual measurements in google Earth I am a little confused as to how this is a right triangle? I see the math you have done but that leaves me a bit bewildered when viewing the actual physical situation.

 

[HOI]

You said, in your original post,
"I plotted 3 points on Google Earth.
West (point A) to slightly North point (point B)= 1284 Km A-B
From Point B to further East Point (point C) = 1717 Km
Then a straight direct line from point C back to point A"

If point B is "slightly north" of point A and point C is "further east" of point C, then angle ABC is a right angle. I don't see how the "map" you show has anything to do with your original description.

 

[Kruidnootje]

If point B is "slightly north" of point A and point C is "further east" of point C, then angle ABC is a right angle. I don't see how the "map" you show has anything to do with your original description.

Well I suppose it would appear that I should have said, A is west, B is the upper middle point and C is East. Then C back to A is a straight line. I am sorry if the original description was mis-leading you, regardless though, the question still remains now does this make your calculations wrong, or are they correct because you have allowed for something that I missed?
Thankyou countryboy