### Fill-In Scribe Post

Since this is just a fill-in scribe post, I'll just make it as straightforward as possible and since most of us understand how to do this.

MORE ON AMBIGUOUS CASE TRIANGLES

ex:

How many possible triangles?

* 1 triangle

* the angle is opposite the longer side

ex.

sin Y / 5 = sin 42 / 3

sin y = 1.1

* no triangles.

* /sin x/ > 1.

ex.

Find all possible values for side c.

5 / sin 28 = 6 / sin B

5 sin B / 5 = 6 sin 28 / 5

sin B = 6 sin 28 / 5

angle B = 34.3 degrees

To find the related angle:

B

_{r}= 180 - 34.3

B

_{r}= 145.7 degrees

There are two possible answers for angle C:

angle C = 180 - 28 - 34.3

angle C = 117.7 degrees

for the related angle:

angle C

_{r}= 180 - 28 - 145.7

angle C

_{r}= 6.3 degrees

Since there are two possible answers for angle C, we organize our work into a table.

when angle C = 117.7 degrees: c / sin 117.7 = 5 / sin 28 c sin 28 = 5 sin 117.7 c = 9.4 | when angle C = 6.3 degrees: c / sin 6.3 = 5 / sin 28 c sin 28 = 5 sin 6.3 c = 1.2 |

last example: Find all possible angles for angle C.

19 / sin 19 = 23 / sin B

19 sin B = 23 sin 16

sin B = 23 sin 16 / 19

angle B = 19.5 degrees

Solving for the related angle:

angle B

_{r}= 180 - 19.5

angle B

_{r}= 160.5 degrees

Solving for angle C:

when angle B = 19.5 degrees: angle C = 180 - 16 - 19.5 angle C = 144.5 degrees | when angle B = 160.5 degrees angle C = 180 - 160.5 - 16 angle C = 3.5 degrees |

And that's the end of today's lesson. I hope that helps.

Er.. do I have to pick a scribe for tomorrow? If I have to.. well, I pick:

rus-L. You can do it!