**Napier's rule**. : either of two

**rules**in spherical trigonometry: the sine of any part is equal to the product of the tangents of the adjacent parts and the sine of any part is equal to the product of the cosines of the opposite parts.

Likewise, people ask, what is Napier's formula?

Then **Napier** has two rules: The sine of a part is equal to the product of the tangents of the two adjacent parts. The sine of a part is equal to the product of the cosines of the two opposite parts.

Subsequently, question is, what is right spherical triangle? A **right spherical triangle**, on the other hand, is a **spherical triangle** whose one of its angles measures 90°. **Spherical triangles** are labeled with angles A, B and C, and respective sides a, b, and c opposite these angles. For **right spherical triangles**, it is customary to set C = 90°.

Additionally, what is Napier's analogy?

Definition of **Napier's analogies**. : four formulas giving the tangent of half the sum or difference of two of the angles or sides of a spherical triangle in terms of the others.

How many degrees are in a spherical triangle?

180°

## What are the properties of spherical triangle?

**angles**of a spherical triangle must together be more than 180° and less than 540° . 7. The greater side is opposite the greater angle , if tow sides are equal their opposite

**angles**are equal . , and if one side of the triangle 90° it is called a quadrantal triangle .

## What is oblique spherical triangle?

**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 the law of tangents used for?

**law of tangents**can be

**used to**compute the missing side and angles of a triangle in which two sides a and b and the enclosed angle γ are given. From. one can compute α − β; together with α + β = 180° − γ this yields α and β; the remaining side c can then be computed using the

**law**of sines.

## What is Polar triangle?

**polar triangle**. : a spherical

**triangle**formed by the arcs of three great circles each of whose poles is the vertex of a given spherical

**triangle**.

## How do you define angles?

**angle**is the figure formed by two rays, called the sides of the

**angle**, sharing a common endpoint, called the vertex of the

**angle**.

**Angles**formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane.

## How do you find the area of a spherical triangle?

**Area**. Let R be the radius of the

**sphere**on which a

**triangle**resides. If angles are measured in radians, the

**area**of a

**triangle**is simply R

^{2}E where E is the

**spherical**excess, defined above. In degrees the formula for

**area**is πR

^{2}E/180.

## What is a triangle on a sphere called?

**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 spherical trigonometry used for?

**Spherical trigonometry**is the branch of

**spherical**geometry that deals with the relationships between

**trigonometric**functions of the sides and angles of the

**spherical**polygons (especially

**spherical**triangles) defined by a number of intersecting great circles on the sphere.

## What is spherical excess?

**spherical excess**. : the amount by which the sum of the three angles of a

**spherical**triangle exceeds two right angles.

## Who discovered spherical trigonometry?

## Why is spherical geometry important?

**Spherical geometry**is

**important**in navigation, because the shortest distance between two points on a sphere is the path along a great circle. Riemannian Postulate: Given a line and a point not on the line, every line passing though the point intersects the line.

## How do you find the angle measure of a sphere?

**Area and angles on a sphere**

- If A, B, and C are the interior angles of a triangle on a unit sphere, the excess (A+B+C) – Pi is exactly equal to the area of the triangle.
- The area of a sector with vertex angle A (measured in radians) is 4 Pi * A / 2 Pi = 2 A.
- The defect of any polygonal figure on a unit sphere is equal to its area.

## What makes up a sphere?

**sphere**is a geometrical figure that is perfectly round, 3-dimensional and circular – like a ball. Geometrically, a

**sphere**is defined as the set of all points equidistant from a single point in space.

## How many angles are in a sphere?

^{o}of 360

^{o}in a

**sphere**. Edit: maybe 180 not that i think about it. A circle would only have to make a half turn. Degrees are used to measure in two dimensions.

## Can a triangle have 270 degrees?

**270**–

**degree triangle**is possible when it is not limited to two dimensions.

## What is the maximum angle of a triangle?

**triangle**has an

**angle**sum of 180 degrees. Therefore the total

**angle**sum of the quadrilateral is 360 degrees.

## How is spherical geometry used in real life?

**Spherical Geometry**is also known as

**hyperbolic geometry**and has many

**real world applications**. One of the most

**used geometry**is

**Spherical Geometry**which describes the surface of a sphere.

**Spherical Geometry**is

**used**by pilots and ship captains as they navigate around the

**world**.

## What is a line segment on a sphere?

**Lines**. As in plane geometry, a

**line**–

**segment on a sphere**is the shortest ‘

**line**‘ connecting two points – over the surface of the

**sphere**. So the maximum ‘extension' of a

**line**–

**segment**(and therefore our

**line**) is a circle, with the same radius as the

**sphere**.

## Can triangles have more than 180 degrees?

**longer**true that the sum of the angles of a

**triangle**is always

**180 degrees**. Very small

**triangles will have**angles summing to only a little

**more than 180 degrees**(because, from the perspective of a very small

**triangle**, the surface of a sphere is nearly flat).