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 a triangle with sides a, b, and c, and angle C opposite side c:
c^2 = a^2 + b^2 - 2ab*cos(C)
Applying this formula to triangle XYZ, where side X = 16cm, side Y = 14cm, and side Z = 15cm, we can solve for angle X.
Plugging in the values, we have:
16^2 = 14^2 + 15^2 - 2*14*15*cos(X)
Simplifying:
256 = 196 + 225 - 420*cos(X)
256 = 421 - 420*cos(X)
Rearranging to isolate cos(X):
420*cos(X) = 421 - 256
420*cos(X) = 165
cos(X) = 165/420
cos(X) = 0.392857
To find X, we take the inverse cosine (arc cosine) of 0.392857:
X = acos(0.392857)
X ≈ 67.52 degrees
To convert this to degrees and minutes, we know that there are 60 minutes in one degree. Therefore:
0.52 degrees = 0.52 * 60 = 31.2 minutes
So, the size of angle X is approximately 67 degrees and 31 minutes.