Question

lprove that cosine rule theorem
for hav board exam​

Answer 1

Laws of Cosine or Cosine Rules

As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –

a2=b2+c2−2bccosx

b2=a2+c2−2accosy

c2=a2+b2−2abcosz

To find the angles x, y & z, these formulae can be re-written as :

cosx=b2+c2−a22bc

cosy=a2+c2−b22ac

cosz=a2+b2–c22ab

Answer 2

Laws of Cosine or Cosine Rules

As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –

a2=b2+c2−2bccosx

b2=a2+c2−2accosy

c2=a2+b2−2abcosz

To find the angles x, y & z, these formulae can be re-written as :

cosx=b2+c2−a22bc

cosy=a2+c2−b22ac

cosz=a2+b2–c22ab

____________________________

Example -Find the length x in the following figure.


Solution: By applying the Cosine rule, we get:

x2=222+282–2.22.28cos97

x2=1418.143

x2=1418.143<