Relations Between Sides and Angles of a Triangles, Objectives, Sine Formula
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Objectives
After studying this lesson, you will be able to:

Studying Lesson
Sine Formula
In , the angles corresponding to the vertices and are denoted by and and the sides opposite to these vertices are denoted by and respectively. These angles and sides are called six elements of the triangle.
Prove that in any triangle, the lengths of the sides are proportional to the sines of the angles opposite to the sides,
Proof:
In in Fig. [(i), (ii), (iii)] and and is acute angle in (i), right angle in (ii) and obtuse angle in (iii).

Sine Formula
Draw perpendicular to (or produced, if need be)
In or
In in fig (i)
Or
In fig (ii) and
and
And fig (iii) and
Or or and
Thus, in all three figures, and
From (iii), we get
Similarly, by drawing perpendiculars from on , we can prove that
From (iv) and (v), we get
(A) is called the sine-formula
Example:
In any triangle, show that
Solution:
We have (Say)
L.H.S.
L.H.S. R.H.S.