Explanation:
Based on the given information:
Side b = 5 cm
Angle A = 64 degrees
Angle B = 38 degrees
To solve for the missing values, we can use the Law of Sines and the Law of Cosines.
a. To find side a using the Law of Sines:
We can use the formula: sin(A) / a = sin(B) / b
sin(64°) / a = sin(38°) / 5
To solve for a, we can rearrange the equation:
a = (sin(64°) * 5) / sin(38°)
b. To find side c using the Law of Cosines:
We can use the formula: c^2 = a^2 + b^2 - 2ab * cos(C)
First, we need to find angle C using the fact that the sum of angles in a triangle is 180 degrees:
C = 180° - A - B
C = 180° - 64° - 38°
Once we have angle C, we can substitute the known values into the Law of Cosines equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
Now, we can solve for c.
c. To find angle C using the Law of Sines:
We can use the formula: sin(C) / c = sin(A) / a
sin(C) / c = sin(64°) / a
To solve for angle C, we can rearrange the equation:
C = arcsin((sin(64°) * c) / a)
Please note that the specific calculations will depend on the values of a, c, and the trigonometric functions used.