An Old Man’s Face or Lover’s Embrace? 3-22-19 T4.2a To define and use the three possibilities for the Law of Sines with SSA Do you see the optical illusion? An Old Man’s Face or Lover’s Embrace?

Active Learning Assignment?

Solve the triangle given: A = 42°, a = 6 cm, b = 12 cm LESSON: Solve the triangle given: A = 42°, a = 6 cm, b = 12 cm C 42° 6 A = _______ a = _______ B = _______ b = _______ C = _______ c = _______ b a 12 B A c Ө Now, we will go to edit mode.

6 12 42 9 9

Given: SSA. Acute Angle. Side opposite the given angle is shorter than the adjacent side. Then, ONE OF 3 possibilities exist: No triangle—opposite side is too short (error message). Right triangle—opposite side is exactly the height of the triangle (one of the angles is 90°). Two triangles—opposite side is longer than height (AMBIGUOUS CASE!!!!!!!!).

Solve the triangle given: A = 42°, a = 9 cm, b = 12 cm (1 dec. pl.) B1 = ______ b1 = __12___ C1 = ______ c1 = _______ 12 63.1° 9 9 42° 63.1° B1 74.9° 13 A1 C1 = 180° – 42° – 63.1° c1 But, there is a secret, hidden extra triangle!

Solve the triangle given: A = 42°, a = 9 cm, b = 12 cm (1 dec. pl.) B2 = ______ b2 = __12___ C2 = ______ c2 = _______ C2 12 116.9° 9 9 42° B2 63.1° 63.1° B1 21.1° 4.8 c2 A1&2 If B1 is 63.1° and the pink triangle is an isosceles triangle, then the opposite angle is also 63.1° . How would you find angle B2? B2 = 180° – 63.1° C2 = 180° – 42° – 116.9°

Active Learning Assignment: If you do not finish, complete at home. Pair up and look over problems 1-28 on Handout T3.2a. Pick out which ones have these: SSA. Acute Angle. Side opposite the given angle is shorter than the adjacent side. If you do not finish, complete at home.