Answer:
Part 1) The measure of angle P is 115°
Part 2) The measure of side RQ is [tex]68.3\ cm[/tex]
Step-by-step explanation:
step 1
Find the measure of angle P
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
∠R+∠P+∠Q=180°
substitute the values
33°+∠P+32°=180°
∠P=180°-65°=115°
step 2
Find the measure of side RQ
Applying the law of cosines
[tex]RQ^{2}=RP^{2}+PQ^{2}-2(RP)(PQ)cos(P)[/tex]
substitute the values
[tex]RQ^{2}=42^{2}+39^{2}-2(42)(39)cos(115\°)[/tex]
[tex]RQ^{2}=4,669.50[/tex]
[tex]RQ=68.3\ cm[/tex]
