Answer:
To determine the missing parts of the triangle, we can use the law of cosines, which states that for a triangle with sides of lengths a, b, and c and angles opposite those sides of A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab cos(C)
b^2 = a^2 + c^2 - 2ac cos(B)
a^2 = b^2 + c^2 - 2bc cos(A)
Using the given values of a, b, and c, we can solve for the angles A, B, and C.
a = 8.1 in
b = 13.3 in
c = 16.2 in
c^2 = a^2 + b^2 - 2ab cos(C)
cos(C) = (a^2 + b^2 - c^2) / (2ab)
cos(C) = (8.1^2 + 13.3^2 - 16.2^2) / (2 * 8.1 * 13.3)
cos(C) = 0.421
C = cos^-1(0.421)
C ≈ 97.3°
b^2 = a^2 + c^2 - 2ac cos(B)
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(B) = (8.1^2 + 16.2^2 - 13.3^2) / (2 * 8.1 * 16.2)
cos(B) = 0.268
B = cos^-1(0.268)
B ≈ 54.8°
We can find angle A by using the fact that the sum of the angles in a triangle is 180°:
A = 180° - B - C
A = 180° - 54.8° - 97.3°
A ≈ 27.9°
Therefore, the missing parts of the triangle are:
A ≈ 27.9°
B ≈ 54.8°
C ≈ 97.3°
So, the answer is option 1.