Answer :
Final answer:
The side lengths of the triangle are approximately a is 5.77, b is 65.82, and c is 121.97, the measure of angle A is 4 degrees.
Explanation:
To solve the triangle, we can use the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees. Given the angle measures of c=114 degrees, a=67, and b=62, we can first find the measure of angle A by subtracting the measures of angles B and C from 180: A = 180 - 62 - 114 = 4 degrees. Next, we can find the remaining side lengths using the Law of Sines. Let's use side a as the reference side:
Sin(A)/a = Sin(B)/b = Sin(C)/c
Sin(4)/67 = Sin(62)/62 = Sin(114)/c
By cross-multiplying, we can solve for the remaining side lengths:
a = (Sin(4) * 67) / Sin(62) = 5.77
b = (Sin(62) * 67) / Sin(4) = 65.82
c = (Sin(114) * 67) / Sin(4) = 121.97
Therefore, the side lengths of the triangle are approximately a = 5.77, b = 65.82, and c = 121.97. The measure of angle A is 4 degrees.
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