## Profile

Join date: Jan 11, 2022

The sine theorem

The sine theorem connects opposite quantities (sides and angles) in a general triangle - do my home work . If two opposite quantities are given, the opposite quantity can be calculated for a third. Along with the cosine theorem, the sine theorem is one of the most important theorems in trigonometry.

In any triangle - math problem solver , the lengths of two sides behave like the sine values of the opposite angles. sine values of the opposite angles:

a : b : c = sin α : sin β : sin γ or asin α=bsin β=csin γ

Proof

1st case:

It holds:

sin β=h ca and sin α=h cb

h c=a⋅sin β and h c=b⋅sin α

It follows that:

a - sinβ = b - sinα or a : b = sinα : sinβ.

2nd case:

It holds:

h c= a - sinβ and h c = b.

Since sin α=1, hc=b⋅sin α.

It follows that:

a - sinβ = b - sinα or a : b = sinα : sinβ.

3rd case:

It holds:

sin δ = sin (180° - α ) = sinα = h c : b and sinβ = h c : a.

From this follows: sin αsin β =abbzw. a : b = sinα : sinβ

A plane figure enclosed by four lines is called a quadrilateral. The four lines are the sides of the quadrilateral. Each two adjacent sides have a corner point in common - homework help geometry . If two lines have another point in common apart from the end points, the quadrilateral is called overlapped. A quadrilateral is called convex if for every two points in the interior of the quadrilateral their connecting line also lies completely in the interior of the quadrilateral.

Natural numbers, historical

Optics

Biochemistry history

Democracies in the EU

The software development cycle

a

More actions