1. 1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

2. There is group of formulas that work for most triangles.b a c B C A h

3. Requirements when using the Law of Sines:
You must be given two angles and any side: AAS or ASA OR
Two sides and an angle opposite one of them: SSA
The Law of Sines does not work for SSS or SAS

4. Find all sides and angles if C = 102.3°, B = 28.7°, and b = 27.4 feet.
27.4 ft
102.3° b a A
49.0°
28.7° B c

5. A pole tilts toward the sun at an angle of 8°
A pole tilts toward the sun at an angle of 8°. If it casts a 22 foot shadow and the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole? b
a = ? c B C A
39°
43°
shadow
98°
= 22 ft

6. You will get no triangle
When you are given two sides and a non-included angle (SSA) – three possibilities exist a b
You will get no triangle
You will get one triangle a b a b a b
You will get two triangles

7. Find all angles if A = 85°, a = 15, and b = 25 ft.C
25 ft b a
= 15 ft A
85° B c
This does not exist so there is no triangle.

8. Find all angles if A = 20.5°, a = 12, and b = 31 feet.C
44.3°
31 ft
94.7 ° b a
= 12 ft
20.5°
115.2° A
20.5°
64.8 ° B c
This happens twice on (0°,180°)

9. Use the Law of Sines to find B:C 8 6
87° B A
With Sine there may be an angle in Quad II that also works so you must check the supplement:
This is too large to be a triangle with the 87 given

10. Use the Law of Sines to find B:C
3.5 4
60° B A
Check the supplement:
The data makes two triangles since both 81.8 & 98.2 work with 60

11. Use the Law of Sines to find C:
100
67° B A
125
No triangle will be formed with these numbers.

12. Draw a triangle for each and use the Law of Sines to decide how many triangles are formed
B = 47°, b = 4, c = No Triangle
C = 60°, b = 30, c = 50 One Triangle
3) B = 20°, a = 12, b = Two triangles
4) B = 37.3°, b = 12.5, c = Two triangles
5) A = 102°, a = 5, c = No triangles

13. Basic Steps for working with Law of Sines
Draw and label a figure
Use Law of Sines with the parts you are given
When you find an angle (Sin-1) check if the supplement also makes a triangle
Find all missing parts that are requested.