Post1330_section7o3 - with 2ft 10ft 30 a b A = = = o find the length of the other side and the measure of the remaining angles Example 4 Find B 45

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Section 7.3 – Laws of Sines and Laws of Cosines 1 Section 7.3 Law of Sines and Law of Cosines We use these laws to find angles and side lengths for triangles of any type (not just right triangles). Law of Sines Example 1: Find x . a , b , c are lengths of sides A , B , C are angles ( A is opposite a , etc.) Law of Sines : The sines of angles are proportional to the lengths of opposite sides. sin sin sin A B C a b c = = Used for SAA , SSA cases. SAA – One side and two angles SSA – Two sides and an angle opposite one of the given sides 50cm x 135 o 30 o A B C a c b
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Section 7.3 – Laws of Sines and Laws of Cosines 2 Note : SSA case is called the ambiguous case of the law of sines. There may be two solutions, one solution, or no solutions. You should throw out the results that don’t make sense. That is, if sin 1 A or the angles add up to more than 180 o . Example 2: Find all possible measures for the indicated angle of the triangle. DEF d = 25 mm e = 13 mm E = 21 o Find D. Example 3: For triangle ABC
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Unformatted text preview: , with 2ft, 10ft, 30 a b A = = = o , find the length of the other side and the measure of the remaining angles. Example 4: Find B . 45 o B 8m 4 2 m Section 7.3 – Laws of Sines and Laws of Cosines 3 Law of Cosines Example 5: Given ∆ PEZ, p = 6 cm, e = 13 cm, and z = 11 cm. Find ∠ Z. a , b , c are lengths of sides A , B , C are angles ( A is opposite a , etc.) Law of Cosines : Generalized Pythagorean theorem. 2 2 2 2 2 2 2 2 2 2 cos 2 cos 2 cos c a b ab C b a c ac B a b c bc A = +-= +-= +-Used for SAS , SSS cases. SAS – Two sides and the included angle SSS – Three sides A B C a c b Section 7.3 – Laws of Sines and Laws of Cosines 4 Example 6: Given ∆ RUN, r = 7 cm, u = 12 cm, and n = 4 cm. Find ∠ U. Example 7: Two sailboats leave the same dock together traveling on courses that have an angle of ° 135 between them. If each sailboat has traveled 3 miles, how far apart are the sailboats from each other?...
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.

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Post1330_section7o3 - with 2ft 10ft 30 a b A = = = o find the length of the other side and the measure of the remaining angles Example 4 Find B 45

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