Answer:
A = 90°
B = 37°
C = 53°
Step-by-step explanation:
Given three sides of a triangle, the Law of Cosines can be used to find the angles.
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For angle A (the largest), we can use ...
a² = b² +c² -2bc·cos(A)
Solving for A, we get ...
A = arccos((b² +c² -a²)/(2bc)) = arccos((3² +4² -5²)/(2·3·4)) = arccos(0)
A = 90°
We can use a similar equation for angle B:
B = arccos((a² +c² -b²)/(2ac)) = arccos((25 +16 -9)/(2·5.4)) = arccos(4/5)
B ≈ 37°
The sum of angles is 180°, so ...
C = 180° -90° -37°
C = 53°
