The Law of Cosines
1 Use the Law of Cosines to Solve Oblique Triangles
-$$\mathrm { a } = 7 , \mathrm {~b} = 14 , \mathrm { c } = 16$$
A) $\mathrm { A } = 26 ^ { \circ } , \mathrm { B } = 61 ^ { \circ } , \mathrm { C } = 93 ^ { \circ }$
B) $\mathrm { A } = 28 ^ { \circ } , \mathrm { B } = 59 ^ { \circ } , \mathrm { C } = 93 ^ { \circ }$
C) $\mathrm { A } = 24 ^ { \circ } , \mathrm { B } = 61 ^ { \circ } , \mathrm { C } = 95 ^ { \circ }$
D) no triangle

Question

Quizplus · Accepted Answer

The Law of Cosines is used to find the angles of a triangle when the lengths of all three sides are known. Given $a = 7$, $b = 14$, and $c = 16$, we can calculate the angles using the formula $\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}$, $\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}$, and $\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$. Calculating these will give the angles closest to the ones in option A, indicating that a triangle with these side lengths is possible and its angles are as stated in option A.

The Law of Cosines 1 Use the Law of Cosines a=7, b=14,c=16\mathrm { a } = 7 , \mathrm {~b} = 14 , \mathrm { c } = 16a=7, b=14,c=16

The Law of Cosines
1 Use the Law of Cosines $\mathrm { a } = 7 , \mathrm {~b} = 14 , \mathrm { c } = 16$