April 4 th copyright2009merrydavidson CALCULATOR TODAY Happy Summer Birthdays to: Timmy Manley: 7/5 th Andrew Krasner: 8/14 th

OBLIQUE TRIANGLES 6.1 & 6.2 A triangle with NO right angles. ANGLES/CAPITAL LETTERS sides/small letters A B C a b c little a is across from Big A put calculator in degree mode

SOLVE the triangle Means to find the length of all sides and the measure of all angles. To solve oblique triangles two pieces of information are needed and a TRIG FUNCTION. Round sides to the nearest TENTH and angles to the nearest DEGREE unless otherwise noted.

LAW OF SINES (you will use 2 of the 3 sections to make a proportion. Memorize this…….. This formula states that the ratio of any side of a triangle to the sine of the angle opposite that side is a constant (proportional) for a given triangle.

EX 1: Given triangle ABC with the measures shown below, find b? 57 O 49 O A B C 8 START with a chart. Fill in what you know Find angle C. Solve the proportion 74 bsin74 = 8sin57 b = 8sin57 sin74 approx 7.0 a= b= c= A= B= C= a= b= c=8 A= 49 B=57 C=

EX 2:In triangle ABC if A = 32 , B = 57 , and c = 14. Find angle C and sides a and b. a =b =c = A =B =C = You do this one. In a minute I will show you the answer.

EX 3: In triangle ABC, A = 110 0, b = 7 and a = 9. Find angle B. a =b =c = A =B =C = 7sin110 = 9sinB sinB = 7sin110 9 Use sine inverse

EX 4: Given an oblique triangle with angle A = 49 0, and side a = 8 and side b = 9, find angle B. a =b =c = A =B =C = You do this one. In a minute I will show you the answer.

EX 5: Find b a = 10b =c = 7 A =B = 51C = B C 10 7 b 51 O A a =b =c = A =B =C = You can not make a proportion 

LAW OF COSINES is used when you can not make a proportion. 6.2 a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 –2ac cos B c 2 = a 2 + b 2 – 2ab cos C Memorize these……..

EX 5: Find b B C 10 7 b 51 O A a = 10b =c = 7 A =B = 51C = Using the law of cosines….. b 2 = a 2 + c 2 -2ac cos B b 2 = (10)(7) cos 51

EX 6: SOLVE the triangle. A B C a = 4b = 5c = 7 A =B =C = Always find the “biggest” angle first! So find C. “store” this to find the other parts. c 2 = a 2 + b 2 -2ab cos C 7 2 = (4)(4) cos C 49 = 41-2(4)(4) cos C 8 = -2(4)(4) cos C

EX 6: SOLVE the triangle. A B C a = 4b = 5c = 7 A =B =C = 104 Now use Law of Sines to find A or B. Then use the sum of angles in a triangle is 180 o to find the other angle.

EX 7: SOLVE the triangle. B C 6 8 b 60 O A a =b =c = A =B =C = What should you find first??? little b Store this! Now find angle A or C.

EX 8: Find cos X; given x = 5, y = 3 and z = 6 in triangle XYZ. x =y =z = X =Y =Z =

HW: WS and work on TAKS packet for additional help on law of sines and/or cosines, go to the internet or come in to see me.