University:
High School
Course:
High School Algebra
Academic year:

2020
Views:

52

Pages:

3
Author:

Arnav Floyd

Law of Sines and Cosines What if, you don't have а right triangle???! Core Concepts Area of а Triangle The area of any triangle is given Ьу one-half the product of the lengths of two sides times the sine of their included angle. For ЛАВС shown, there are three ways to calculate the area. ь в А Ь с Area = ½ ас sinB Area = ½ Ьс sinA Area = ½ аЬ sin С Theorems Theorem 9.9 LawofSines The Law of Sines can Ье written in either of the following forms for ЛАВС with sides of length а, Ь, and с. в sinA = " ro.-ho м = siп • с of Theorem 9.1 О e"-c.h с- 11 J S,� а = -- sinA � i'(.. = �11 -- siл rk. с S'i� Lawof Cosines If Л АВС has sides of length а, Ь, and с, as shown, then the following are true. а2 = Ь2 + с2 - 2Ьс cos А А Ь а 2 + с2 - 2ас cos 1]3 с2 = а2 + Ь 2 - 2аЬ cos С ь с с - tt"� Extra Practice ��(.,' ln Exercises 1-3, use а calculator to find the trigonometric ratio. 1. sin 225 ° 2. cos 111 -.70 7 \ -,- ° 3. ��'б- 3 --'1.5/ /..-/5 \ - -. r; 11_] �lt7� - ln Exercises 4 and 5, find the area of the triangle. С 5. F 19 G D � ie..� : {_e.d(s;nL.) ::- t tan 96° CJ� P•I ( s,·A 74) -;._ '1•7 (;��2) i (siri F) (q ' \q , - � S, 11 Z, 2, ( � l�r'\ (.t,, о 7 ') l- '1) о о 1 r.1 Solve the triangle. Round decimal answers to the nearest tenth. 6. А S•" 5'D Р.,с.. .i4A-+�\1 +�с...::. 5"0 � ;о t� /�о с_:. \уС) --- ,,. \ ' 2 7,., ( $ 11'\ \()С, ) }1 (!., :: --- .. . .. ... - s ;,-1 �о [АВ � ;(iзз� ..,.,,_ ,-.г-:;. вс... ::. 33.7/ ,_.., .,.. " " , �� •.; �,• ,; � .. �.....·-· •' Solve the triangle. Round decimal answers to the nearest tenth. 7. lt +х. В +'"�L ,� � �� + 3�.';°1;) +-� (_ -s-,2. -�'L -��.1� �" t&c;-: � А 16 в 25 - "s '1.1 С 5%,'=' 7-:: � с_ 1 ---&-2..- � il'\ _,. ZS' Si"' В ----- /'Ь - 1 ь ( s; �1,.\ � �� ( � , ,.. В) f\ �'"@rc-(� -j--�i""vs," ' . &J ,\ if\ �s С - z J. 5'fo. 7 -:. 4ti. � 2. 1.. +- ; - 2- ( JJ( (. 2,, � r '1 - ;o(c.os 13) � -��1 -: '1 - Ч i.[tc,5 f.t) '1 -=- - 1- _i..l � • l.t '1 - .l.-S- '1 - 30 {cos В) - с, /� =- -3о( oS В) Z.. "'( () 5 � 7 + 3 ... 2. ( 7) ( � с о 5 ft l-{ -:. 1,,t Di r q. .. "1 z.(tos А) ""2- ----- -- :i \ "�r a"'-�l�s r� L--.et � +- с os;" t'5 v-vN� у��л d() ,,..0 -1- A�vL. у"""' � ми �4- "'--� 2- Sма-� -s ;·'f'\ i•;.. s.-�-1[1ь(::ъ, � = В -:. ::,'1. 3 ,,� 7 � ( sr" S &-. t. i) А В:. '-� (�,f\ �.'-i) '}. А А& S,';\&-� (' ":) 8. •bt Sif\ А- в ( �, � � '2-\ � � S' .,, tf" �;г. _- �;1\ -3?>:. -ч2. (cos ,4) .., � t,1 coS - ,,, С,.. cos"' [, 7%g -=- [cos (о�""'(.7&-�'):. А А] \�-: �А +413 +�С. 1 W :: • 1 �,,1 • ?,�,11 -(р С) ьо +-4( &.()