1. Warm – Up
Solve the following triangles for the missing side or angle: 1) 2) 3) 9 10 x
27°
32° 14 8 x
48°

2. Law of Sines
Section 6.1

3. Objectives Students will be able to…
Solve oblique triangles using the Law of Sines (including the ambiguous case)
Solve application problems for all triangles using trigonometry

4. Homework
Law of Sines Worksheet - EVENS

5. Oblique Triangles Triangles without a right angle Four Cases:
Two angles and any side (AAS or ASA)
Two sides and an angle opposite one of them (SSA) (ambiguous case)
Three sides (SSS)
Two sides and their included angle (SAS)
First 2 cases can be solved using the Law of Sines A B C a b c

6. Law Of Sines If ABC is a triangle with sides a, b, and c, then
𝑎 𝑠𝑖𝑛𝐴 = 𝑏 𝑠𝑖𝑛𝐵 = 𝑐 𝑠𝑖𝑛𝐶
*Can be written as 𝑠𝑖𝑛𝐴 𝑎 = 𝑠𝑖𝑛𝐵 𝑏 = 𝑠𝑖𝑛𝐶 𝑐 A B C a b c A B C a b c

7. Example - AAS
Given C = 102.3°, B = 28.7° and b = 27.4 feet, find the remaining angles and sides A B C a b c

8. Example - ASA
A pole tilts toward the sun at an 8° angle from the vertical and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43°. How tall is the pole?

9. Ambiguous Case - SSA
In a triangle where you are given a, b and h (h = b sinA)
If angle A is acute
And a < h – no triangle is possible
And a = h – one triangle is possible (right triangle)
And a ≥ b – one triangle is possible
And h < a < b – two triangles are possible
If angle A is obtuse
And a ≤ b – no triangle is possible
And a > b – one triangle is possible

10. Example
Given a = 15, b = 25, and A = 85°, solve the triangle.

11. Example
Given a = 22 in, b = 12 in, and A = 42°, find the remaining side and angles.

12. Example
Solve the triangle, given a = 12 m, b = 31 m, and A = 20.5°.

14. Example
A bridge is to be built across a small lake from a gazebo to the dock is S 41° W. From a tree 100m from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E respectively. Find the distance from the gazebo to the dock. T G D

15. Practice
Law of Sines Worksheet

16. Closure
Given A = 102.4°, C = 16.7°, and a = 21.6, solve for the remaining angle and sides