BQ #1: Unit P Concept 2 and 4: Law of Sines SSA and Oblique Triangles

2. Law of Sines- Side Side Angle (SSA) is an ambigious case not like AAS or ASA. When dealing with SSA the three angles are not all known as easily as the others because we only know ONE angle out of the three. It is amigious because it can be three different types: one triangle, two triangles, or no triangle at all.

One Triangle 

As seen in the picture above there is only one possible triangle for this problem. We know there is not a second triangle because angle A and Angle C add up to 325.9 which is way past 180 degrees so therefore there is no second triangle because it is greater than 180.

Two Traingles 

As seen in the picture above this example has two possible triangles. We know there are two triangles because the law of sines means there is one angle in the first quadrant and another angle in the second quadrant. We find the second angle (the prime angle) by subtracting the first angle we got by 180.

No Triangle 

As seen in the picture above this example has no possible triangles. We know there are no possible triangles because once we used the law of sines with SSA, we got sinC: 1.75 and we know from the previous unit that sin can not be greater than 1 so therefore that leads to no solution. Another reason we know a triangle has no solution is when there is more than one obtuse angle.

4. Area Formulas- The area of an oblique triangle is derived from the formula for the area of a trianlge which is A=1/2bh. It area of an oblique triangle is one-half of the product of two sides and the sine of the angle the problem gives you. So basically the three types of equations can be A=1/2bcSinA, A=1/2acSinB, and A=1/2abSinC. It relates to the formula we are familar with by substituting in our h in the normal equation with the a side and sine of an angle given. We just have to make sure when we have our equation, all the letters are different.