length of adjacent side when theta=6deg23'55

A:length of opposite side when hypotenuse= 17.03metres & theta =6deg23'55"

B:length of opposite side when hypotenuse= 13.23metres & theta =7deg37'

C:length of opposite side when hypotenuse= 20.35metres & theta =5deg38'40"

A

6° 23' 55"   convert to decimal degrees

[ 6 +  23/60 + 55/3600]  ≈ 6.399°

So  

sin (6.399)  =  opp / 17.03       multiply both sides by 17.03

17.03 sin (6.399)  = opp ≈  1.9 m

B

7° 37'  =  [ 7 + 37/60]   ≈ 7.62°

13.23 sin (7.62)  = opp ≈ 1.76m  

C

5° 38' 40"   =  [ 5 + 38/60 + 40/3600 ]  ≈ 5.64°

20.35 sin (5.64 )   = opp ≈  2 m