Answer :
The angles of triangle ABC are approximately 23°, 33°, and 26°.
Given:
a = 66
b = 25
c = 45
Using the Law of Cosines:
[tex]c^2[/tex] = [tex]a^2[/tex] + [tex]b^2[/tex] - 2ab cos(C)
45^2 = 66^2 + 25^2 - 2(66)(25) cos(C)
2025 = 4356 + 625 - 3300 cos(C)
2025 = 4981 - 3300 cos(C)
-2956 = -3300 cos(C)
cos(C) = 0.8957
C = 26°
Using the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
66/sin(A) = 25/sin(B) = 45/sin(26°)
sin(A) = 66 * sin(26°) / 45 = 0.3846
A = 23°
Using the Law of Sines again:
b/sin(B) = c/sin(C)
25/sin(B) = 45/sin(26°)
sin(B) = 25 * sin(26°) / 45 = 0.5556
B = 33°
Therefore, the angles of triangle ABC are approximately 23°, 33°, and 26°.
