Question

The length of side RP is approximately 42 cm.

Answer 1

Answer:

Part 1) The measure of angle P is 115°

Part 2) The measure of side RQ is $68.3\ cm$

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

$RQ^{2}=RP^{2}+PQ^{2}-2(RP)(PQ)cos(P)$

substitute the values

$RQ^{2}=42^{2}+39^{2}-2(42)(39)cos(115\°)$

$RQ^{2}=4,669.50$

$RQ=68.3\ cm$