Question

Solve each triangle using either the Law of Sines or the Law of Cosines. If no triangle exists, write “no solution.” Round your answers to the nearest tenth:
a = 12, b = 14, c = 21
A = 51°, b = 41, c = 40
A = 23°, B = 55°, b = 9
A = 18°, a = 25, b = 18

Answer 1

Question 1

Uses the law of cosines

\[cos(A) = \frac{b^2 +c^2-a^2}{2bc}\]

once you have A you can use the law of sines to find a 2nd angle then the angle sum of a triangle for the 3rd angle.

Question 2

Law of cosines

\[a^2 = b^2 + c^2 - 2bc \cos(A)\]

Question 3

law of sines

\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\]

Question 4

Law of Sine

hope it helps... just substitute and evaluate

Answer 2

i just need 3 and 4

Answer 3

Cosine Law: c² = a² + b² – 2ab cos C
Sine Law: Sine a / a = Sine b / b = sine c / c

Question 1,
you have a, b, and c. You can use the cosine law to solve for angle A, B, and C.

Question 2:
You can rewrite the cosine law to A² = B² + C² - 2BC cos A
and solve for angle A. After you have the angle, you can use sine law to solve for angle B and C.

Question 3:
You can use Sine law to solve for A, and you can calculate angle C (sum of triangle) and thus length of C using the Cosine law

Question 4:
Similar to Question 3. Use Sine law to solve for angle B, and thus angle C, and then C using cosine