Solve a Triangle Given Two Sides and the

Solve a Triangle Given Two Sides and the Included Angle Step 1 Use the Law of Cosines to find c. c 2 = a 2 + b 2 – 2 ab cos C Law of Cosines c 2 = 72 + 102 – 2(7)(10) cos 73° a = 7, b = 10, and C = 73º c 2 108. 1 c 10. 4 Simplify using a calculator. Take the square root of each side.

Solve a Triangle Given Two Sides and the Included Angle Step 2 Use the Law of Sines to find the measure of angle A. Law of Sines A = 7, C = 73°, and c 10. 4 Multiply each side by 7. Use a calculator. Use the sin– 1 function.

Solve a Triangle Given Two Sides and the Included Angle Step 3 Find the measure of angle B. m B = 180° – (40° + 73°) or 67° Answer: Therefore, c 10. 4, A 40°, and B 67°.

Solve a Triangle Given Three Sides Solve ΔABC. Step 1 Use the Law of Cosines to find the measure of the largest angle first, angle C. c 2 = a 2 + b 2 – 2 ab cos C 122 = 92 + 72 – 2(9)(7) cos C Law of Cosines a = 9, b = 7, and c = 12

Solve a Triangle Given Three Sides 122 – 92 – 72= – 2(9)(7) cos C Subtract 92 and 72 from each side. Divide each side by – 126. – 0. 1111 cos C 96° C Use a calculator. Use the cos– 1 function.

Solve a Triangle Given Three Sides Step 2 Use the Law of Sines to find the measure of angle B. Law of Sines b = 7, C 96°, and c = 12 Multiply each side by 7. Use a calculator. Use the sin– 1 function.

Solve a Triangle Given Three Sides Step 3 Find the measure of angle A. m A = 180° – (35° + 96°) or 49° Answer: Therefore, A 49°, B 35°, and C 96°.