Please help me find the angles of thes triangles?

Question

a = 2 ft, b = 3 ft, c = 4 ft

a = 9.3 cm, b = 5.7 cm, c = 8.2 cm

a = 42.9 m, b = 37.6 m, c = 62.7 m

AB = 1240 ft. AC = 876 ft, BC = 918 ft

Answer 1

Hint:  use law of cosines

Answer 2

Cos(C) = (a^2 + b^2 - c^2 ) / (2ab)

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

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

Cos(C) = (4+9-16) / (2*2*3) = -(3/12)

Cos(C) = -1/4 radians

Arccos(-.25) = C

C = 1.82 radians

Cos(B) = (4+16-9) / (2*2*4) = 11/16

Cos(B) = 11/16

Arccos(11/16) = B

B = .81 radians

Cos(A) = (9+16-4) / (2*3*4) = 21/24 = 7/8

Cos(A) = 7/8

Arccos(7/8) = A

A = .51 radians

Converting radians to degrees:

C = 1.82 radians * (180/pi) = 104.3 degrees

C = 104.3 degrees

B = .81 radians * (180/pi) = 46.4 degrees

B = 46.4 degrees

A = .51 radians * (180/pi) = 29.2 degrees

A = 29.2 degrees

Check your work:

104.3 degrees + 46.4 degrees + 29.2 degrees = 179.9 degrees

Rounded this equals 180 degrees, which should be the sum of all the angles in a triangle if calculated correctly.

Doing the other problems is just a matter of simple substitution and following the example.  Good luck =)