Section 5.7: The Ambiguous Case of the Law of Sines September 16, 2014 5-7: Solving Triangles for Ambiguous Cases of the Law of Sines (SSA combination) 1.) Decide how many solutions there are Remember, this only matters if you are given SSA. Otherwise, just solve! 2.) Use the Law of Sines to find an angle first. 3.) Find the other angle and the last side. Sep 238:44 AM height - drawn from the vertex between the two given sides 1.) A = 36°, a = 2, c = 7 Sep 238:53 AM Section 5.7: The Ambiguous Case of the Law of Sines September 16, 2014 height - drawn from the vertex between the two given sides 2.) B = 106°, a = 17, b = 25 Sep 238:53 AM Construction #3: Suppose ∠A is acute & side a is smaller than side c Recall from yesterday the constructions in which two triangles were formed from SSA Sep 238:51 AM Section 5.7: The Ambiguous Case of the Law of Sines September 16, 2014 Construction #3: Suppose ∠A is acute & side a is smaller than side c Recall from yesterday the constructions in which two triangles were formed from SSA Sep 238:51 AM The only way to get two solutions This is very rare! Only happens with 1 out of the 6 SSA combinations! Angle-Side-Side Given angle is acute opposite side is smaller than adjacent, but bigger than the height. c a Find angle "C" by the Law of Sines then solve that triangle A For the second triangle take 180-"C", then solve that triangle. c a "C" = angle across from the adjacent side A Sep 247:27 AM Section 5.7: The Ambiguous Case of the Law of Sines September 16, 2014 The only way to get two solutions This is very rare! Only happens with 1 out of the 6 SSA combinations! Angle-Side-Side Given angle is acute opposite side is smaller than adjacent, but bigger than the height. c Find angle "C" by the Law of Sines then solve that triangle a A For the second triangle take 180-"C", then solve that triangle. c a "C" = angle across from the adjacent side A Sep 247:27 AM height - drawn from the vertex between the two given sides 3.) B = 37°, a = 32, b = 27 Sep 238:53 AM Section 5.7: The Ambiguous Case of the Law of Sines September 16, 2014 height - drawn from the vertex between the two given sides 4.) C = 90°, a = 8, c = 7 Sep 238:53 AM height - drawn from the vertex between the two given sides 5.) A = 58°, C = 94°, b = 17 Sep 238:53 AM

© Copyright 2021 Paperzz