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Step 1: Draw a triangle Step 2: Label your smallest angle A Step 3: Label your medium angle B Step 4: Label your largest angle C Step 5: Label your side opposite angle A, a Step 6: Label your side opposite angle B, b Step 7: Label your side opposite angle C, c What do you recall from Geometry about the sides opposite the angles? What makes a triangle oblique? How is trigonometry useful to solve and find the areas of oblique triangles? What situations create the ambiguous case for the Law of Sines? What is a directional bearing and how is it applied to real life situations? How do you use trigonometric functions to solve real life problems? The student will be able to understand and apply solving real world applications using laws of sine and cosine for oblique triangles. Do Now Law of Sines Break Practice Closure Homework 𝑏 𝑐 𝑎 = = 𝑆𝑆𝑆 𝐴 𝑆𝑆𝑆 𝐵 𝑆𝑆𝑆 𝐶 What does it mean? Calculate the measure of ALL the angles Calculate the measure of ALL the sides What Any triangle that does not have a right angle How are they? do you solve them? You need to know the measure of at least one side and the measure of any two other parts. AAS or ASA – Law of Sines SSA – Law of Sines SSS – Law of Cosines SAS – Law of Cosines Why is this important? Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical (90°). At a point 30 meters from the tree, the angle of elevation to the top of the tree is 22.5°. Find the height of the tree. SSA No such triangle exists One triangle exists Two distinct triangles exists How can you minimize mistakes? Draw a picture! Solve the given triangle(s) A = 60° a=4 b = 14 Solve the given triangle(s) A = 58° a = 4.5 b=5 The area of ANY triangle is one-half the product of the length of two sides times the sine of their included angle: 𝐴𝐴𝐴𝐴 = 𝐴𝐴𝐴𝐴 = 𝐴𝐴𝐴𝐴 = 1 𝑏𝑏 𝑆𝑆𝑆 𝐴 2 1 𝑎𝑐 𝑆𝑆𝑆 𝐵 2 1 𝑎𝑏 𝑆𝑆𝑆 𝐶 2 Find the area of a triangular lot with side lengths that measure 24 yards and 18 yards and form an 80° angle. On a small lake, a child swam from point A to point B at a bearing of N 28°E. The child then swam to point C at a bearing of N 58°W. Point C is 800 meters due north of point A. How many total meters did the child swim? How do you use trigonometry to solve and find the areas of oblique triangles? Textbook pages 414-415 #11-23 ODD, 25, 26