Download presentation

Presentation is loading. Please wait.

Published byBlake Unwin Modified over 2 years ago

1
LAW OF SINES: THE AMBIGUOUS CASE

2
MENTAL DRILL Identify if the given oblique triangle can be solved using the Law of Sines or the Law of Cosines 1. X = 21 0, Z = 65 0 and y = 34.7 2. s = 73.1, r = 93.67 and T = 65 0 3. a = 78.3, b = 23.5 and c = 36.8 /ctr Law of Sines Law of Cosines

3
AMBIGUOUS Open to various interpretations Having double meaning Difficult to classify, distinguish, or comprehend /ctr

4
RECALL: Opposite sides of angles of a triangle Interior Angles of a Triangle Theorem Triangle Inequality Theorem /ctr

5
RECALL: Oblique Triangles Triangles that do not have right angles (acute or obtuse triangles) /ctr

6
RECALL: LAW OF SINE – 1 sin 1 /ctr

7
RECALL: Sine values of supplementary angles are equal. Example: Sin 80 o = 0.9848 Sin 100 o = 0.9848 /ctr

8
Law of Sines: The Ambiguous Case Given: lengths of two sides and the angle opposite one of them (S-S-A) /ctr

9
Possible Outcomes Case 1: If A is acute and a < b A C B b a c h = b sin A a. If a < b sinA A C B b a c h NO SOLUTION

10
Possible Outcomes Case 1: If A is acute and a < b AC B b a c h = b sin A b. If a = b sinA A C B b = a c h 1 SOLUTION

11
Possible Outcomes Case 1: If A is acute and a < b AC B ba c h = b sin A c. If a > b sinA A C B b c h 2 SOLUTIONS aa B 180 -

12
Possible Outcomes Case 2: If A is acute and a > b C B h 1 SOLUTION ba A AC B ba c h = b sin A

13
Possible Outcomes Case 3: If A is obtuse and a > b C A B a b c ONE SOLUTION

14
Possible Outcomes Case 3: If A is obtuse and a ≤ b C A B a b c NO SOLUTION

15
First, determine what case you have. (ASA, AAS, SSA, etc.) Law of Sines (“plug & chug”) determine # of solutions ASA, AAS SSA use the Law of Sines to find them.

16
For SSA Triangles: 1. If A < 90° a.a < b 1.a < b(sin A)No Solution 2.a = b(sin A)1 Solution 3.a > b(sin A)2 Solution b.a ≥ b1 Solution 2. If A ≥ 90° a.a ≤ bNo Solution b.a > b1 Solution

17
Given: ABC where a = 22 inches b = 12 inches m A = 42 o EXAMPLE 1 Find m B, m C, and c. (acute) a>b m A > m B SINGLE–SOLUTION CASE

18
sin A = sin B a b Sin B 0.36498 m B = 21.41 o or 21 o Sine values of supplementary angles are equal. The supplement of B is B 2. m B 2 =159 o

19
m C = 180 o – (42 o + 21 o ) m C = 117 o sin A = sin C a c c = 29.29 inches SINGLE–SOLUTION CASE

20
Given: ABC where c = 15 inches b = 25 inches m C = 85 o EXAMPLE 2 Find m B, m C, and c. (acute) c < b c ? b sin C 15 < 25 sin 85 o NO SOLUTION CASE

21
sin A = sin B a b /ctr Sin B 1.66032 m B = ? Sin B > 1 NOT POSSIBLE ! Recall: – 1 sin 1 NO SOLUTION CASE

22
Given: ABC where b = 15.2 inches a = 20 inches m B = 110 o EXAMPLE 3 Find m B, m C, and c. (obtuse) b < a NO SOLUTION CASE

23
sin A = sin B a b /ctr Sin B 1.23644 m B = ? Sin B > 1 NOT POSSIBLE ! Recall: – 1 sin 1 NO SOLUTION CASE

24
Given: ABC where a = 24 inches b = 36 inches m A = 25 o EXAMPLE 4 Find m B, m C, and c. (acute) a < b a ? b sin A24 > 36 sin 25 o TWO – SOLUTION CASE

25
sin A = sin B a b Sin B 0.63393 m B = 39.34 o or 39 o The supplement of B is B 2. m B 2 = 141 o m C 1 = 180 o – (25 o + 39 o ) m C 1 = 116 o m C 2 = 180 o – (25 o +141 o ) m C 2 = 14 o

26
sin A = sin C a c 1 /ctr c 1 = 51.04 inches sin A = sin C a c 2 c = 13.74 inches

27
Final Answers: m B 1 = 39 o m C 1 = 116 o c 1 = 51.04 in. EXAMPLE 3 TWO – SOLUTION CASE m B 2 = 141 o m C 2 = 14 o C 2 = 13.74 in. /ctr

28
CLASSWORK: (notebook) Find m B, m C, and c, if they exist. 1 ) a = 9.1, b = 12, m A = 35 o 2) a = 25, b = 46, m A = 37 o 3) a = 15, b = 10, m A = 66 o /ctr

29
Answers: 1 )Case 1: m B=49 o,m C=96 o,c=15.78 Case 2: m B=131 o,m C=14 o,c=3.84 2)No possible solution. 3)m B=38 o,m C=76 o,c=15.93

Similar presentations

Presentation is loading. Please wait....

OK

FUNCTIONS OF ANY ANGLE, OBLIQUE TRIANGLES

FUNCTIONS OF ANY ANGLE, OBLIQUE TRIANGLES

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on marriott group of hotels Ppt on nuclear micro batteries Ppt on some new technology Ppt on 2nd world war flags Ppt on obesity prevention activities Ppt on english chapters of class 11 Download ppt on civil disobedience movement in 1930 Ppt on indian cricket history Ppt on history generation and classification of computer Ppt on bank lending statistics