Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Learning Goal: I can solve word problems using Sine Law while considering the possibility of the Ambiguous.

Unit 4: Trigonometry

Minds On

• Using a ruler and a protractor, draw a triangle that has a side length of 10cm, another side length of 8cm, and the angle opposite the 8cm side is 30.

• Use your ruler and protractor to determine the measures of the other two angles and the third side.


Learning Goal:

I can solve word problems using Sine Law while considering the possibility of the Ambiguous Case.

Lesson 5 – Word Problems and the Ambiguous Case



Given information What can be Found

Law Required

1. Two angles and any side (AAS or ASA)

2. Two sides and the contained angle (SAS)

3. Three Sides (SSS)

4. Two sides and an angle opposite one of them (SSA)

For Oblique (non-right) Triangles


Ambiguous: "Unclear or inexact because a choice between alternatives has not been made.“

The ambiguous case arises when we use Sine Law for SSA.




Whenever you want to use Sine Law to determine an angle when you are given SSA, you need to consider the ambiguous case. If you are given two angles (AAS, or ASA) you do not need to worry about ambiguity.



With SSA there are three possibilities:

• No triangle exists

• Only one triangle exists

• Two triangles exist



1. No triangle existsIf the “swinging arm” of the triangle is less than the height of the triangle, then no solution exists. With the swinging arm being shorter than the height it will never reach the base of the triangle.



2. One triangle existsIf the “swinging arm” of the triangle is equal to the height of the triangle, then only one solution exists. With the swinging arm being equal to the height it will only reach the base of the triangle once (when it is perpendicular to the base)

Also, when the swinging side is greater than or equal to the other known side, there is also only one solution.



3. Two triangles existsIf the “swinging arm” of the triangle is greater than the height of the triangle, then two solutions exists. With the swinging arm being greater than the height it will reach the base of the triangle twice. Once making an acute angle with the base, and once making an obtuse angle with the base.


Determine angle C



Determine angle C


A

B

30°a = 10c = 16


Determine angle CLesson 5 – Word Problems and the Ambiguous

Case

A

B

C30°

a = 10c = 16


What are angles of depression and angles of elevation?







Lesson 5 – Word Problems

Homework

Pg. 254 #6, 11, 12, 14, 15

Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Learning Goal: I can solve word problems using Sine Law while considering the possibility of the Ambiguous.

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