Lesson 37 continued Get out your notes from yesterday

AccPreCalc Lesson 37 Essential Question: Law of Sines… what kind of Amazingness is that? What Is the null case of the law of sines? What is the ambiguous case? Standard: MCC9‐12.G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. MCC9‐12.G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non‐right triangles (e.g., surveying problems, resultant forces).

Write the Area formula for triangles in three ways A = ½ ac sin(B) = ½ bc sin(A) = ½ ab sin(C) C a b B A c

Now set all of those formulas equal to each other and divide by abc… Now set all of those formulas equal to each other and divide by abc…. You should get the Law of Sines

AAS ASA SSA – three cases: You can only solve triangles using law of sines if they are one of the three cases AAS ASA SSA – three cases: 1. one solution 2. no solution 3. 2 solutions

Lets say you know side a, b, and Angle A. Then one of three cases occur

When Solving a SSA Let’s say you know You can only change the angle when the opposite side length is known. Also a general rule is no two angles can sum to greater than 180 degrees A 22 30 C B 15

Given triangle PWS, SW = 16 cm , P = 68 degrees, WP = 18.5 cm. Find PS. No Solution case!!!

Given Triangle ABC, where A = 20 degrees, a = 12, and c = 31 solve the triangle. Two Solutions

Example :  a = 10, b = 16, and m<A = 30º.  How many distinct triangles can be drawn given these measurements