The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
-$$a = 8 , b = 6 , c = 4$$
A) $\mathrm { A } = 104 ^ { \circ } , \mathrm { B } = 47 ^ { \circ } , \mathrm { C } = 29 ^ { \circ }$
B) $\mathrm { A } = 47 ^ { \circ } , \mathrm { B } = 104 ^ { \circ } , \mathrm { C } = 29 ^ { \circ }$
C) $\mathrm { A } = 104 ^ { \circ } , \mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 47 ^ { \circ }$
D) $\mathrm { A } = 47 ^ { \circ } , \mathrm { B } = 29 ^ { \circ } , \mathrm { C } = 104 ^ { \circ }$

Question

Quizplus · Accepted Answer

The Law of Cosines states that in a triangle with sides a, b, and c, and opposite angles A, B, and C, the following equation holds:c^2 = a^2 + b^2 - 2ab cos(C)Using this equation, we can solve for angle C:cos(C) = (a^2 + b^2 - c^2) / 2abPlugging in the given values, we get:cos(C) = (8^2 + 6^2 - 4^2) / 2(8)(6) = 1/4Therefore, C = 75.5 degrees.We can then use the Law of Sines to solve for angles A and B:sin(A) / a = sin(C) / csin(B) / b = sin(C) / cPlugging in the given values, we get:sin(A) = (sin(75.5) * 8) / 4 = 1.93sin(B) = (sin(75.5) * 6) / 4 = 1.45However, since sin(A) and sin(B) are both greater than 1, there is no solution for angles A and B. Therefore, the correct answer is none of the choices provided.

The Law of Cosines 1 Use the Law of Cosines a=8,b=6,c=4a = 8 , b = 6 , c = 4a=8,b=6,c=4

The Law of Cosines
1 Use the Law of Cosines $a = 8 , b = 6 , c = 4$