What if the triangle information is given in profane form (oops!!) 8-2 Law of Sines What if the triangle information is given in profane form (oops!!)

Try this Solve ΔABC if a = 50, c = 65 and A = 57º What happened? a c Fixed A b

What happened? The data was such that the triangle is just impossible. Are there other possibilities? Yes: there are 4

a too short a just perfect a just a little bigger a too big to hit twice

a < csinA a = csinA A csinA < a < c a ≥ c a c c a A A b b c a

How do we deal with this? Remember: The calculator only gives the Q1 answer (function theory). SO, you have to figure out what the Q2 answer would be and see if the triangle can still exist. Q1 + Q2 = 180

What is the process to follow? If ASS triangle (given 1 angle) Determine second angle. Determine what third angle would be with given and second angles. Determine second angle’s supplement. Determine what third angle would be with given angle and second angle’s supplement. * Determine the last side based both on the last angle (step 2) and other option (step 4)

Examples The first example we did, where you get “error” or “E” as a solution – that means that there is no triangle possible. Solve for ΔABC if c = 65, a = 60 and A = 57º 3. Solve for ΔABC if c = 65, a = 68 and