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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) C 540 a 3.0, 4.0, LA = C = Solve triangle ABC. (If an answer does not exist,, enter DNE. Round your answers to one decimal place.) b 69 35, LA 72° C = C = a = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a 28, b = 39, c 29 LA = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) = 17, 13, c 22 a = LA= o Sketch the triangle 500 LA B 770 C = 270 c 270 50° 77 50° 770 270 A A A 770 50° 270 270 50° 77 C A Solve the triangle using the Law of Sines. (Round side lengths to the nearest integer.) a = b Sketch the triangle. 100° LA = 270, C=60 C 100° 60 100° 27 27° C 60 C C 270 60 100° 27 100° A 60 A Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.) a = b =

Respuesta :

The dimensions of the triangle ΔABC are;

a = 3.0, b = 4.0, ∠C = 54°

The law of cosines indicates that we get;

c² = b² + a² - 2·b·a·cos(∠C)

Therefore;

c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893

c ≈ √(10.893) ≈ 3.3

The law of sines indicates that we get;

sin(54°)/3.3 = sin(∠A)/3.0

∠A = arcsine(3 × sin(54°)/3.3) ≈ 47.35°

∠B = 180° - 54° - 47.35° ≈ 78.65°

b = 69, c = 35, ∠A = 72°

a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45

a ≈ √(4493.45) ≈ 67.03

The law of sines indicates that we get;

sin(72°)/67.03 = sin(∠B)/69

∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°

∠C = 180° - 72° - 78.24° ≈ 29.76°

∠C  ≈ 29.76°

a = 28, b = 39, c = 29

a² = b² + c² - 2·b·c·cos(A)

cos(A) = (a² - (b² + c²)) ÷ (2·b·c)

Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976
∠A = arccos(0.6976) ≈ 45.77°

sin(45.77)/28 = sin(B)/39

sin(B) = 39 × sin(45.77)/28 ≈ 0.998

∠B = arcsine(0.998) ≈ 86.417°

∠C = 180° - 45.77° - 86.417° = 47.813°

a = 13, b = 17, c = 22

cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807

∠A ≈ arccos(0.807) ≈ 36.15°

sin(36.15)°/13 = sin(∠B)/17

sin(∠B) = 17 × sin(36.15)°/13

∠B =50.48°          

∠C = 180° - 36.15° - 50.48° ≈ 93.37°

The specified triangle is the angle

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