Question

DERIVE THE SINE& COSINE RULE.

Answer 1

Answer:

Derivation of cosine rule

The following are the formulas for cosine law for any triangles with sides a, b, c and angles A, B, C, respectively.

a2=b2+c2−2bccosA

b2=a2+c2−2accosB

c2=a2+b2−2abcosC

Consider the triangle to the right:

Cosine function for triangle ADB

cosA=x/c

x=c cosA

Pythagorean theorem for triangle ADB

x2+h2=c2

h2=c2−x2

Pythagorean theorem for triangle CDB

(b−x)2+h2=a2

Substitute h2 = c2 - x2

(b−x)2+(c2−x2)=a2

(b2−2bx+x2)+(c2−x2)=a2

b2−2bx+c2=a2

Substitute x = c cos A

b2−2b(ccosA)+c2=a2

Rearrange:

a2=b2+c2−2bccosA

The other two formulas can be derived in the same manner.

Answer 2

Step-by-step explanation:

DERIVE THE SINE& COSINE RULE.