Answer:
In triangle XYZ, we are given that YZ = 9ft, XZ = 13ft, and angle X = 111 degrees.
To find the remaining side and angles of the triangle, we can use the Law of Cosines and the Law of Sines.
First, we can use the Law of Cosines to find the length of side XY:
XY^2 = XZ^2 + YZ^2 - 2(XZ)(YZ)cos(X)
XY^2 = 13^2 + 9^2 - 2(13)(9)cos(111)
XY^2 ≈ 5.98
XY ≈ 2.44 ft (rounded to two decimal places)
Next, we can use the Law of Sines to find the measure of angles Y and Z:
sin(Y)/YZ = sin(X)/XY
sin(Y)/9 = sin(111)/2.44
sin(Y) ≈ 0.39
Y ≈ 23.4 degrees (rounded to one decimal place)
sin(Z)/XZ = sin(X)/XY
sin(Z)/13 = sin(111)/2.44
sin(Z) ≈ 0.87
Z ≈ 60.6 degrees (rounded to one decimal place)
Therefore, in triangle XYZ, we have:
• XY ≈ 2.44 ft
• Y ≈ 23.4 degrees
• Z ≈ 60.6 degrees