BQ#1: Unit P Concept 2 & 5 - Law of Sines & Area of an Oblique Triangle

2. Law of Sines

SSA (Side Side Angle) is considered ambiguous because there is no one sure solution. The problem only gives us one angle of the triangle so there is some ambiguity of what the triangle looks like. There could be one possible solution, two possible solutions, or no solutions.

This connects to the Unit Circle trig function values because the Law of Sines can give us the measures for each line segment on the Unit Circle. In Unit N, we learned that the unit circle has a radius that is measured to be one, however, it is not always the case. As a result, the Law of Sines help us correlate the angles with the length of their sides.

4. Area Formulas

The "area of an oblique" triangle is derived from the regular area equation, A=1/2bh. In the triangle below, you can see that there is perpendicular line through the triangle, creating two triangles. If we are looking at angle C, we know from previous units that SinC=h/a , therefore, h=aSinC. Now, just substitute it into the regular area equation: A=1/2b(aSinC). The equation we just found, however, is only if the problem gives you angle C. The equation for angle A: 1/2bcSinA. Equation for Angle B: 1/2acSinB. We use the same process to get the area for angles A and B. This relates to the area we are familiar with because we have to use that equation in order to get the area for an oblique triangle. Like I said before, you plug what h (height) is into the normal area equation.

Resources:

SSS Packet