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3 years ago

SHOW ALL WORK for all points law of cosine

Mathematics

1 answer:

Kruka [31]3 years ago

7 0

Answer:

The answer to your question is below

Step-by-step explanation:

∠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°

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