Consider the triangle ABC. Suppose that a=73 b=71 c=3 Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth

Question

ABC triangle

a between B and C

b between A and C

c between A and B

Answer 1

ABC = 73 71 3

angle c = 2.3873 = about 2.4 degrees

use the Law of cosines

3^2 = 73^2 + 71^2 -2(73)71Cos(c)

solve for c

do the same solving for a and b

73^2 = 71^2 +3^2 - 2(73)(3)Cos(a)

71^2 = 73^2+ 3^2 -2(71)(3)Cos(b)

or use the Law of Sines once you have one angle

Sin2.3873/3 = SinA/73 = SinB/72

smallest angle is opposite the smallest side

largest angle opposite the largest side

c is a very small angle

a and b are about the same size = a little less than 90 degrees each

Answer 2

By cosine law: cosA = (71² +3² - 73²)/(2·71·3); A = cos^-1 [(71² +3² - 73²)/(2·71·3)] = 130.9143° = 130.9°;

By sine law: snC/c = sinA/a; C = sin^-1(3sin130.9143°/73) = 1.7796° = 1.8°;

B = 180° - (130.9143° + 1.7796°) = 47.3061° = 47.3°

Answer 3