Question

How do you determine the number of possible triangles and find the measure of the three angles given `AB=14, BC=21, mangleC=75`?

Answer 1

No Triangle

Explanation:

Since the given information is for a SSA triangle it is the ambiguous case. In the ambiguous case we first find the height by using the formula `h=bsin A`.

Note that A is the given angle and its side is always a so the other side will be b .

So if `A < 90^@` and if

1. `h < a < b` then then there are two solutions or two triangles.

2. `h < b < a` then there is one solution or one triangle.

3. `a < h < b` then there is no solution or no triangle.

If `A >=90^@` and if

1. `a > b` then there is one solution or one triangle.

2. `a <=b` there is no solution

`h=21 sin75^@~~20.28`, since `14 < 20.28 < 21` we have

`a< h < b` so we have no solution or no triangle.