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Pre-Calc Exam Notes 38

Pre-Calc Exam Notes 38 - oblique triangles that is...

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2 General Triangles In Section 1.3 we saw how to solve a right triangle: given two sides, or one side and one acute angle, we could find the remaining sides and angles. In each case we were actually given three pieces of information, since we already knew one angle was 90 . For a general triangle, which may or may not have a right angle, we will again need three pieces of information. The four cases are: Case 1: One side and two angles Case 2: Two sides and one opposite angle Case 3: Two sides and the angle between them Case 4: Three sides Note that if we were given all three angles we could not determine the sides uniquely; by similarity an infinite number of triangles have the same angles. In this chapter we will learn how to solve a general triangle in all four of the above cases. Though the methods described will work for right triangles, they are mostly used to solve
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Unformatted text preview: oblique triangles , that is, triangles which do not have a right angle. There are two types oF oblique triangles: an acute triangle has all acute angles, and an obtuse triangle has one obtuse angle. As we will see, Cases 1 and 2 can be solved using the law of sines , Case 3 can be solved using either the law of cosines or the law of tangents , and Case 4 can be solved using the law oF cosines. 2.1 The Law of Sines Theorem 2.1. Law of Sines: IF a triangle has sides oF lengths a , b , and c opposite the angles A , B , and C , respectively, then a sin A = b sin B = c sin C . (2.1) Note that by taking reciprocals, equation (2.1) can be written as sin A a = sin B b = sin C c , (2.2) and it can also be written as a collection oF three equations: a b = sin A sin B , a c = sin A sin C , b c = sin B sin C (2.3) 38...
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