Projection Formula

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Theorem :

In any triangle ABC, with sides a = BC, b = CA and c = BA, then prove that a = b cos C + c cos B, b = c cos A +    a cos C,  c = a cos B + b cos A

Fig (i)

Fig (ii)

Fig (iii)

Proof:

Let ABC be any triangle and let AD be drawn perpendicular to BC.

(AD = h = altitude of triangle)

In figure (i), we have

BD = x, DC = y

From right-angled triangle ADB, we have

From right-angled triangle ADC, we have

Adding (ii) and (iii), we get

x + y = cos B + b cox C …. (iv)

From (i) and (iv), we have

From figure (ii), we have

BD = x, DC = y

In D ADB,

In D ADC,

From fig (iii),

Hence, a = b cos C + c cos B.

Similarly, other three results can be proved.