The answer to your question is below
Step-by-step explanation:
1)
∠A use rule of cosines
cos A = (15² - 18² - 6²)/-2(6)(18)
cosA = -135/-216
cos A = 0.625
A = 51.31
∠B = rule of cosines
sinB/6 = sinA/ 15
sinB = 6sin51.31/15
sinB = 6(0.052)
sinB = 0.31
B = 18.19
∠C = 180 - 18.19 - 51.31
∠C = 110.5
2) HP² = 27² + 23² - 2(27)(23)cos85
HP² = 729 + 529 - 108.25
HP² = 1149.8
HP = 33.9
sinH/23 = sin85/33.9
sinH = 23sin85/33.9
sinH = 0.675
H = 42.52
P = 180 - 42.52 - 85
P = 52.48
3) xz² = 12² + 29² - 2(12)(29)cos99
xz² = 144 + 841 + 108.9
xz² = 1093.9
xz = 33
sinx/12 = sin99/33
sinx = 12sin99/33
sinx = 0.36
x = 21
Z = 180 - 99 - 21
Z = 60
4) cosP = (30² - 18² - 17²)/ -2(18)(17)
cosP = 287/ -612
cosP = -0.46
P = 118
sinQ/18 = sin118/30
sinQ = 18 sin118/30
sinQ = 0.529
Q = 32°
R = 180 - 32 - 118
R = 30°
5) KH² = 9² + 20.1² - 2(9)(20.1)cos 88.4
KH² = 81 + 404.01 - 10.1
KH² = 474.9
KH = 21.8
sinH/9 = sin88.4/21.8
sinH = 9sin88.4/21.8
sinH = 0.412
H = 24.37°
K = 180 - 24.37 - 88.4
K = 67.23°
6) cos R = (6² - 9² - 14²)/-2(9)(14)
cos R = -241/-252
cosR = 0.956
R = 17
sinS/9 = sin17/6
sinS = 9sin17/6
sinS = 0.438
S = 26°
T = 180 - 26 - 14
T = 140°
7) cos C = (23.6² - 16.2² - 12.3²)/-2(16.2)(12.3)
cosC = 143.23/-398.52
cosC = -0.359
C = 111°
sinB/16.2 = sin111/23.6
sinB = 16.2sin111/23.6
sinB = 0.64
B = 39.9
A = 180 - 39.9 - 111
A = 29.1°
8) cos B = (28² - 17² - 15²)/-2(15)(17)
cos B = 270/-510
cosB = -0,529
B = 122°
sinA/17 = sin122/28
sinA = 17sin122/28
sinA = 0.514
A = 31°
C = 180 -122 - 31
C = 27°
