Question 1182314
 In triangle PQR, P = 50°, PR = 11 and PQ = 9.

a) Show that there are two possible measures of PQR

b) Sketch triangle PQR for each case

c)For each case, find: i) the measure of QPR , ii) the area of the triangle, iii) the perimeter of the triangle.
<pre>Is measure of PQR referring to &#8737PQR? If so, don't you think you need to state that? 
If so and measure of QPR refers to &#8737QPR, which is the same as &#8737P, wasn't that given?
a) Use the 2 given sides, the included angle, and Law of Cosines to find side p (same as side QR).
   This should be around 8.644539 units. Then use the Law of Sines to find &#8737Q, which should be approximately 78.47<sup>o</sup>.   
   With &#8737s P and Q being 50<sup>o</sup>, and 78.47<sup>o</sup>, respectively, &#8737R is then 51.53<sup>o</sup>.
   Note that <font color = red><b><u>&#8737Q, being 78.47<sup>o</sup> can also measure 101.53<sup>o</sup></b></u></font> since its reference angle measures that, in the 2nd quadrant.
   With &#8737Q being 101.53<sup>o</sup>, &#8737P, 50<sup>o</sup>, then &#8737R becomes 28.47<sup>o</sup>. This proves that &#8737Q (same as &#8737PQR) can have 2 measures. 
   This also means that &#8710PQR can either be ACUTE or OBTUSE.
   Note that with 2 sides and an INCLUDED angle given, the requested AREA of this NON-RIGHT triangle can be found
   by using the formula: {{{highlight_green(matrix(1,3, Area, "=", (1/2)ab*Sin (C)))}}}, which in this case would be: {{{highlight_green(matrix(1,3, Area, "=", (1/2)qr*sin (P)))}}}
   You should now be able to answer the other questions.