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To find the size of angle X, we can use the Law of Cosines.
The Law of Cosines states that in any triangle with sides a, b, and c, and angle A opposite side a:
a^2 = b^2 + c^2 - 2bc * cos(A)
Plugging in the values given, we can calculate angle X:
16^2 = 14^2 + 15^2 - 2(14)(15) * cos(X)
Simplifying further:
256 = 196 + 225 - 420 * cos(X)
256 = 421 - 420 * cos(X)
Rearranging the equation:
420 * cos(X) = 421 - 256
420 * cos(X) = 165
cos(X) = 165/420
cos(X) = 0.39285714
Now, we can use the inverse cosine function to find the angle X:
X = cos^(-1)(0.39285714)
X ≈ 67.768 degrees
To get the answer in minutes, we can multiply the decimal part of the angle (0.768) by 60:
Minutes = 0.768 * 60
Minutes ≈ 46
Therefore, the size of angle X is approximately 67 degrees and 46 minutes.