6.1 Law of Sines +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases

Oblique Triangles A is acute A is obtuse A a B b C c A B C a b c

Solving Oblique Triangles To solve oblique triangles you need one of the following cases 2 angles and any side (AAS or ASA) 2 sides and the angle opposite one of them (SSA) 3 sides (SSS) 2 sides and their included angle (SAS)

Law of Sines If ABC is a triangle with sides a, b, and c, then

Example Find the missing sides and angles given the following information C = B = b = 27.4 ft

Word Problem A pole tilts towards the sun at an 8 0 angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is How tall is the pole?

Ambiguous Cases (SSA) (h = bsinA) A is acute a < h no triangles A is acute a = h 1 triangle A a h b A b ah

More Cases A is acute a > b 1 triangle A is acute h < a < b 2 triangles A ba h A b ha a

More Cases A is obtuse a < b no triangles A is obtuse a > b 1 triangle A a b A b a

Example Find the missing sides and angles of the triangle given the following information a = 22 in b = 12 in A = 42 0

Determine how many triangles there would be? 1)A = 62 0, a = 10, b = 12 2)A = 98 0, a = 10, b = 3 3)A = 54 0, a = 7, b = 10

Finding two solutions Find two triangles for which a = 12, b = 31, and A =

Example Find the missing sides and angles for the following information a = 29 b = 46 A = 31 0

Using Sine To Find Area Area of an Oblique Triangle

Find the Area of the Triangle Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102 o.

Word Problem The course for a boat race starts at point A and proceeds in the direction S 52 o W to point B, then in the direction S 40 o E to point C, and finally back to point A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.