What is oblique spherical triangle?

Definition of oblique spherical triangle Spherical triangles are said to be oblique if none of its included angle is 90° or two or three of its included angles are 90°. Spherical triangle with only one included angle equal to 90° is a right triangle.

What is a triangle on a sphere called?

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the spherical analog of the planar triangle, and is sometimes called an Euler triangle (Harris and Stocker 1998).

What is an oblique triangle and illustration?

An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all threee angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).

How do you find the angle of a spherical triangle?

General spherical triangle

1. Law of sines. sin α / sin a = sin β / sin b = sin γ / sin c.
2. Law of cosines. cos a = cos b cos c + sin b sin c cos α cos α = -cos β cos γ + sin β sin γ cos a.
3. Tangents. Let s = (a + b + c)/2 and let σ = (α + β + γ)/2.
4. Area. Let R be the radius of the sphere on which a triangle resides.

How do you solve a right spherical triangle?

For right spherical triangles, it is customary to set C = 90°. One way of solving for the missing sides and angles of a right spherical triangle is using Napier’s rules. Napier’s rules consist of two parts, and are used in conjunction with a figure called Napier’s circle as shown.

What are spherical triangles used for?

Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam.

How many triangles are in a sphere?

, we can fit exactly 3 triangles from the top of the sphere to the bottom, corner to corner, with edges all lying along one great circle. Also note that we can fit up to five triangles around the north pole, each with one vertex at the north pole, since 5α < 2π < 6α.

What are two kinds of oblique triangle?

Oblique triangles are broken into two types: acute triangles and obtuse triangles.

How many cases are in the oblique triangle?

three possible cases
The Law of Sines can be used to solve oblique triangles, which are non-right triangles. According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. There are three possible cases: ASA, AAS, SSA.

What is Napier’s rule of right spherical triangle?

Napier’s rules for right spherical triangles When one of the angles, say C, of a spherical triangle is equal to π/2 the various identities given above are considerably simplified. There are ten identities relating three elements chosen from the set a, b, c, A, B.

How do you use napiers circle?

The rules are aided with the Napier’s circle. In Napier’s circle, the sides and angle of the triangle are written in consecutive order (not including the right angle), and complimentary angles are taken for quantities opposite the right angle.

How do you know if a spherical triangle is oblique?

Spherical triangles are said to be oblique if none of its included angle is 90° or two or three of its included angles are 90°. Spherical triangle with only one included angle equal to 90° is a right triangle.

What is an obtuse oblique triangle?

For example, a triangle whose interior angles are 105º, 60º, and 15º is an obtuse oblique triangle. Note that 105º + 60º + 15º = 180º.

How do you find the measure of an oblique triangle?

For example, a triangle whose interior angles are 105º, 60º, and 15º is an obtuse oblique triangle. Note that 105º + 60º + 15º = 180º. To solve oblique triangles, that is, find the measures of all their sides and all their angles, the theorems of sine and cosine are required.