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**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

**Quadrilateral, general**

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.

**See also:**