Question

The length of side RP is approximately 42 cm.

Answer 1

Part 1) The measure of angle P is 115°

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

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`