Final answer:
To solve a triangle with lengths a=3.6, b=7.7, and c=6.7, use the Law of Cosines to calculate each angle. After finding all angles, confirm they sum to 180°, as this is a requirement for all triangles.
Step-by-step explanation:
To solve the triangle with sides a=3.6, b=7.7, c=6.7, you need to determine the angles of the triangle using the Law of Cosines. The Law of Cosines is given by c² = a² + b² - 2ab*cos(C), where C is the angle opposite side c. Start by solving for one of the angles and then use either the Law of Sines or the Law of Cosines to find the other two angles.
First, let's solve for angle C using the Law of Cosines:
c² = a² + b² - 2ab*cos(C)
6.7² = 3.6² + 7.7² - 2(3.6)(7.7)cos(C)
Once you find the value of cos(C), you can calculate the angle C by taking the inverse cosine. Repeat similar steps to find angles A and B. After calculating all angles, check to ensure their sum equals 180°, as this is a property of all triangles. Please note that there are cases where a triangle with the given side lengths may not exist, such as when the sum of the lengths of two sides is less than the length of the third side.