Use the Law of Cosines to solve each triangle with the given measures.

Question

a = 4.38 ft, b = 3.79 ft, c = 5.22 ft

Answer 1

A triangle has 3 sides and 3 angles.  In this case, we know the 3 sides (a,b,c), so we need to find the 3 angles, (A,B,C).

 

Law of Cosines for angle A:  cos(A) = (-a²+b²+c²)/2bc

 

Plug in the given values for a, b, and c:

 

cos(A) = {-(4.38)²+(3.79)²+(5.22)²}/2(3.79)(5.22)

 

cos(A) = 22.4281/39.5676 = 0.5668

 

A = cos^-1(0.5668) = 55.47^o

 

Law of Cosines for angle B:  cos(B) = (a²-b²+c²)/2ac

 

Solve for angle B in the same way we solved for angle A above: 1) Plug in values for a, b, and c to find cos(B); 2) take the inverse cosine to find angle B.

 

Angle C will be C = 180^o - (A+B)