# Relations Between Sides and Angles of a Triangles, Projection Formula

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## Projection Formula

In, if and , then prove that

(i)

(ii)

(iii)

Proof:

As in previous result, three cases arise. We will discuss them one by one.

(i) When is acute:

In

In

(ii) When :

(iii) When is obtuse:

In

In

In fig (iii)

Thus in all cases,

Similarly, we can prove that

And

Example 1: In any triangle , show that

Solution:

L.H.S.

R.H.S.

Example 2: In any , prove that

Solution:

L.H.S.

R.H.S.