Monday, December 11, 2006

6.5: The Ambiguous Case

Hey everybody, this section is the one called The Ambiguous Case, which sounds scary, but isn't. It means that there are two options for the length of the side opposite an angle on a triangle where you have SSA.

Here is an example, where the red lines are the two options that complete the triangle, assuming that you know the measure of Angle B:

In this situation, the things that are ambiguous are the length of side a and the measure of angle A. The length of side b does not change, but it moves to a different position.

The goal is to find the value of the third side (in this case, A) depending on the measure of angle A.

In order to solve these types of problems, you need to determine the number of solutions that are possible. You can do this by using...

( sin B = b / a ) or ( a sin B = b)

If the answer to that eqation is 0 (zero), then there is 1 (one) answer.

If b > a sin B , then there are 2 answers.

If b is less than a sin B, then there are no real answers.

Example Problems:

1. Find out how many solutions there will be for the missing angle and what they are, if any.

Angle A is 20 degrees, side a is 38 ft and side b is 45 ft.

First: 38 = 45 sin 20 , which becomes 38 = 15.39, so a > b, and there are two solutions.

Second: Use the Law of sine to find the angle measures: sin 20 / 38 = sin B / 45.

The answers you get from that is 23.89, and then you subtract that from 180 to get the other, 156.11.

2. Find the length of the missing side.

In triangel EFG, angle F = 33 degrees, side f = 6 miles, and side e = 5 miles. Find side g.

First: Set up the equation with the law of cosines: 6^2 = 5^2 + g^2 -2(5)(g)cos 33.

This leaves you with 0 = g^2 -8.39g - 11.

Second: solve this using the quadratic formula (under PROGRAMS on the calculator).

On the calculator, A = 1^2, B = -8.39(1) and C = -11.

Since one of the answers is negative, the only answer for side g is 9.54 miles.

If there is still something you don't understand, ask Mr. French or check out this site: http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/lawofsinesambiguouscase.html

Reminder: Henry is next!!! YAY

And finally, if you want to further study math, check out this video...it's funny.

http://youtube.com/watch?v=MiMWJ1xBo8w

Yep, so that's it. Have fun and i'll see you guys on the flip side.

1 Comments:

At 5:55 PM, Blogger Tara said...

That movie was hilarious...we all need some Anti-Garry Gum.

 

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