BQ #1: Unit P Concept 2 Law of Sines & Concept 4 Area Formulas

2.Law of Sines
SSA is ambiguous because we can have one solution, two solutions, or no solution depending on the existing rules of Sines and triangles.

In this first case we have two solutions. This is possible in this type of problem because with the information given we were able to use the Sine of A to solve for the missing pieces. The first thing i did was solve for SinC which equaled to .1573 then took the inverse which gave us the value of the angle of C equal to 9. This problem did not meet any wall that would go against the laws of triangles or sines. It met the requirements of staying within 180 degrees and it Sine was not larger than 1. 

This case deals with one solution. The first thing I did was use Sine B as the main factor to solve for the missing pieces which in this case I solved for the Sine of A. After taking the inverse of SinA I got 8.1 as the angle of the first triangle, then i subtracted 8.1 from 180 to get the value of angle A for the second triangle and this is where I met a wall. Angle B has a value of 101 degrees, there can only be one obtuse angle within a triangle. When I added 101 to 171.9 it went over 180 degrees of a triangle so this meant there was only one solution.

Last example is no solution. This we automatically knew was not going to have any solutions because once we took the SinA it was bigger than one and sine cannot be bigger than 1. 

4.Area Formulas

The area of oblique triangles originated from the area formula of a triangle which is A=1/2bh. We derived it by for example in the triangle below:

http://www.compuhigh.com/demo/lesson07_files/oblique.gif

We took the sinC of triangle number 1 and made it equal to h/a also known as (O)pposite/(H)ypotenuse since were dealing with sine. Then we cross multiplied and got that h=asinC, this is the first part of the total equation now we know the value of h. Next we had to substitute the value of h into the original equation of area of a triangle. It related to the Area formula that I know because it doesnt matter what angle you use, the values will always be consistent. It just depends on the angle in which you are trying to find the area for.

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