13 4 Law of Sines Objectives 1 Solve

13. 4 Law of Sines Objectives: 1. Solve problems by using the Law of Sines 2. Determine whether a triangle has one, two, or no solutions.

The Area of a Triangle This formula allows you to find the area of a triangle when you know the measures of two sides and the included angle. The area of a triangle is one-half the product of the lengths of two sides and the sine of their A included angle: b c B a C

Example Find the area of ΔABC to the nearest tenth. C 6 cm 25° A 3 cm B area=3. 8 cm²

Law of Sines Let ΔABC be any triangle with a, b, and c representing the measure of sides opposite angles with measurements A, B, and C respectively. Then, The L of S works for ANY triangle when you know 2 angles and a side or the measures of two sides and the angle opposite one of them.

Example Solve ΔABC. A=27° c=11. 1 a=5. 1 C 100° a B 53° c 9 A

Possible Triangles Given Two Sides and One Opposite Angle If A is obtuse If A is acute a b b b sin A A a < b sin A no solution b A a a = b sin A one solution b A a<b no solution a a b > a > b sin a two solutions b a>b one solution A a>b one solution

Example In ΔABC, A=25°, a=13, b=12. Determine whether ΔABC has no solution, one solution, or two solutions. Then solve ΔABC. Find b sin A and compare it to a. 12 sin 25=5. 07 13>5. 07 a≥b – one solution

Continued

Homework p. 730 14 -34 even