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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
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What is the contribution of menelaus to trigonometry?
He defined the spherical triangle
What are the 2 branches of trigonometry?
plane trigonometry spherical trigonometry
What is the difference between plane trigonometry and spherical trigonometry?
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
Why does spherical trigonometry important?
The earth, which we live on, is approximately a sphere. It is important, therefore, to know spherical trigonometry.
What is the importance of spherical trigonometry in math?
Historically, it is because we live on a planet which is approximately spherical. 2-dimensional trigonometry was adequate for relatively small shapes where the curvature of the earth had negligible effect. For larger shapes the spherical nature of the earth was important and therefore, so was spherical trigonometry.
What is polar triangle?
The polar triangle is a geometric figure formed by connecting the poles of a spherical triangle to the vertices of that triangle. In spherical geometry, if a triangle is defined by three points on the surface of a sphere, the polar triangle consists of the points that are the poles of the arcs connecting these vertices. This concept is useful in various applications of spherical trigonometry, particularly in navigation and astronomy, where understanding the relationships between angles and distances on a sphere is crucial. The relationships between the angles and sides of the polar triangle can be derived from those of the original spherical triangle.
What is the contribution of menelaus to trigonometry?
He defined the spherical triangle
What are the 2 branches of trigonometry?
plane trigonometry spherical trigonometry
What is the difference between plane trigonometry and spherical trigonometry?
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
Why does spherical trigonometry important?
The earth, which we live on, is approximately a sphere. It is important, therefore, to know spherical trigonometry.
What is the meaning of spherical triangle?
Spherical trigonometry is a branch of spherical geometry, which deals with polygons (especially triangles) on the sphere and the relationships between the sides and the angles. This is of great importance for calculations in astronomy and earth-surface and orbital and space navigation.
How many kinds of trigonometry are there in mathematics?
Two types of trigonometry are recognized: planar and spherical. Planar is 2-dimensional, while spherical is 3-dimensional. Though these are different fields, spherical trigonometry is really just an application of planar trigonometry in several planes.
What is the importance of spherical trigonometry in math?
Historically, it is because we live on a planet which is approximately spherical. 2-dimensional trigonometry was adequate for relatively small shapes where the curvature of the earth had negligible effect. For larger shapes the spherical nature of the earth was important and therefore, so was spherical trigonometry.
Is a triangle still a triangle if it has 2 obtuse angles?
Only if it is drawn in 3-dimension. A triangle drawn in 2-dimension does NOT satisfy the criteria. However, a triangle drawen across the surface of a sphere, such as the Earth, does satisfy the criteria.
What is the importance of spherical trigonometry?
For navigational purposes
How do you solve for a spherical triangle?
If by sperical triangle you mean a triangle on the surface of a sphere, you will need 3 dimensional coordinate geometry. Whether you use polar coordinates or linear coordinates will depend on what you want to "solve".
What is soh cah toa in trigonometry?
SoH: used for finding the sine of a triangle in trigonometry: Opposite/HypotenuseCaH: used for finding the cosine of a triangle in trigonometry: Adjacent/HypotenuseToA: used for finding the tangent of a triangle in trigonometry: Opposite/Adjacent
