It's an equilateral triangle whose legs are all 90-degree arcs. Here's a quadrantal triangle on the earth: -- Start at the north Pole. -- Draw the first side, down along the north 1/2 of the Prime Meridian to the equator. -- Draw the second side westward along the equator, to 90 degrees west longitude. -- Draw the third side straight north, back up to the north Pole. Each side of the triangle is 90 degrees, each interior angle is also 90 degrees, and the sum of its interior angles is 270 degrees. Pretty weird.
Three non-collinear points do not determine a unique spherical triangle.
A plane triangle looks like a common triangle. A plane triangle is solved with linear units. A spherical triangle is found inside of a sphere. This type of triangle is solved with angular units.
All three interior angles of a spherical triangle may be right angles.
He defined the spherical triangle
It's an equilateral triangle whose legs are all 90-degree arcs. Here's a quadrantal triangle on the earth: -- Start at the north Pole. -- Draw the first side, down along the north 1/2 of the Prime Meridian to the equator. -- Draw the second side westward along the equator, to 90 degrees west longitude. -- Draw the third side straight north, back up to the north Pole. Each side of the triangle is 90 degrees, each interior angle is also 90 degrees, and the sum of its interior angles is 270 degrees. Pretty weird.
Three non-collinear points do not determine a unique spherical triangle.
A plane triangle looks like a common triangle. A plane triangle is solved with linear units. A spherical triangle is found inside of a sphere. This type of triangle is solved with angular units.
Yes, they do exist.
In spherical trigonometry this is possible
All three interior angles of a spherical triangle may be right angles.
He defined the spherical triangle
for any spherical triangle on any sphere there associated another triangle called the polar triangle associated with this spherical triangle with the property that the sum of any angle (or side) of one of these two triangles and the length of the side (and the angle)of the other triangle is alway equil to 180 degrees
The solutions do depend on what the questions are!
A spherical triangle is not a question or a puzzle that you can solve, or even slove! You need to specify what information you have and what you wish to solve for: angles, lengths of sides, perimeter, area and so on.
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In normal geometry, it's not possible to make a triangle with two obtuse angles. It is possible to make a triangle with two obtuse angles in spherical geometry -- it's a kind of "spherical triangle". It is possible to make a triangle with two obtuse angles in some kinds of non-Euclidean geometry -- it's a kind of "non-Euclidean triangle".