Final answer:
To find the remaining angles B and C in the triangle with sides a=6, b=8, and included angle A=150°, we can use the Law of Cosines to find the third side c. Then, we can use the Law of Sines to find angles B and C.
Step-by-step explanation:
The given triangle has sides a = 6, b = 8, and an included angle A = 150 degrees.
To find the remaining angles B and C, we can use the Law of Cosines. According to the Law of Cosines, c^2 = a^2 + b^2 - 2ab*cos(A).
Substituting the given values, we have c^2 = 6^2 + 8^2 - 2*6*8*cos(150).
Solving this equation gives us c^2 = 56, and taking the square root gives us c = 7.48 (rounded to two decimal places).
Now, we can use the Law of Sines to find the remaining angles. According to the Law of Sines, sin(A)/a = sin(B)/b = sin(C)/c.
Setting up the equation, we have sin(150)/6 = sin(B)/8 = sin(C)/7.48.
Solving for sin(B) and sin(C), we find sin(B) = 0.5 and sin(C) = 0.63 (rounded to two decimal places).
Using inverse sine, we can find the values of angles B and C as B = arcsin(0.5) ≈ 30.1 degrees and C = arcsin(0.63) ≈ 48.7 degrees.
Therefore, the correct solution for a triangle with sides a = 6, b = 8, and included angle A = 150 degrees is B ≈ 30.1° and C ≈ 48.7°.