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Answer :
Using the Law of Cosines and Law of Sines, the length of side a is about 6.2 units, while the angles B and C are approximately 51.5 degrees and 66.5 degrees, respectively.
To solve the triangle ABC, given b=5, c=6, and A=62 degrees, we can use the Law of Cosines. First, we calculate the length of side a using the formula a^2 = b^2 + c^2 - 2bc * cos(A). Plugging in values, we get a^2 = 5^2 + 6^2 - 2 * 5 * 6* cos(62 degrees). After evaluating, we find the value of a.
Next, to find the other angles B and C, we can use the Law of Sines or apply the Law of Cosines again. Since the sum of angles in any triangle is 180 degrees, after finding one more angle, the third angle can be found by subtracting the known angles from 180 degrees.
The final answer for the length of side a is approximately 6.2 units, the angle B is approximately 51.5 degrees, and the angle C is approximately 66.5 degrees. It is important to round each answer to the nearest tenth as requested.
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