In triangle XYZ, side X=16cm side Y=14cm and side Z=15cm . Calculate the size of angle X to the nearest degrees and minute?
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.