Ambiguity

From the Compact Oxford English Dictionary:

• noun (pl. ambiguities) uncertain or inexact meaning.

But first ... a review of triangles.

Solving right triangles:

Solving triangles using the Sine Law:

Solving triangles using the Cosine Law:

The ambiguous case triangle - when the given angle is opposite the shorter of the two given sides, there may be ambiguity.

For example: how many triangles ∆ABC can we draw where ÐC = 100

0, b = 10 and

c = 8?

How many triangles ∆ABC can we draw where ÐC = 30

0, b = 10 and c = 4?

How many triangles ∆ABC can we draw where ÐC = 30

0, b = 10 and c = 5?

How many triangles ∆ABC can we draw where ÐC = 30

0, b = 10 and c = 12?

Practice:

Exercise 10, p. 22, Questions 2 - 6.

Homework:

Exercise 10, Question 1.Exercise 11, Questions 1 and 2.

Pretest tomorrowTest on WednesdayStart next unit (Algebra) on Thursday!