Cosine Rule is used:

When the length of all 3 sides of a triangle is given. OR

When 2 sides and an included angle is given. (C is an included angle of lines 43 cm and 90 cm.)

Cosine is a trigonometric function used to calculate angles of a right-angled triangle. However, the cosine rule can be used for all types of triangles including acute angled, right-angled, and obtuse-angled triangles.

a^{2} = b^{2 }+ c^{2} - 2bc cos A

b^{2} = a^{2} + c^{2} - 2ac cos B

c^{2} = b^{2} + c^{2} - 2ab cos C

a^{2} = b^{2} + c^{2} - 2bc cos A

a^{2} + 2bc cos A = b^{2} + c^{2} - 2bc cos A + 2bc cos A (add 2bc cos A on both sides)

a^{2} - a^{2} + 2bc cos A = b^{2} + c^{2} - a^{2} (subtract a^{2} on both sides)

2bc cos A = b^{2} + c^{2} - a^{2} (divide 2bc on both sides)

cos A= (b^2 + c^2 - a^(2 ))/2bc

cos A= (b^2 + c^2 - a^(2 ))/2bc

cos B= (a^2 + c^2 - b^(2 ))/2ac

cos C= (a^2 + b^2 - c^(2 ))/2ac

Any angle can be labelled as A, B or C.

The side opposite to angle A is labelled a, the side opposite to angle B is labelled

b, and the side opposite to angle C is labelled c.

In the triangle, a = 43 cm, b = 90 cm, c = 51 cm.

To calculate angle A:

cos A= (b^{2} + c^{2} - a^{2} /2bc

cos A= (90^{2} + 51^{2} - 43^{2} /(2*51*90)

cos A= 0.964

A= cos^{-1} (0.964)

A=15.420571°