Solve triangle ABC Round the length to three declmal places

Solve triangle ABC. (Round the length to three declmal places and the angles to one decimal place.) 13 21 120 Need Help?W Need Help? WacTalk tos Tutor Save Progress Another Version 28. O-1.65 points STrig2 3.6.012 Solve triangle ABC. (Round your answers to one decimal place.) 4B 12 40 41

Solution

1) let b = 13, a= 21

length AB = c = ?

angle C = 120 degree

from law of cosine:

c² = b² + a² -2 *b*a* cos C

c² = ( 13)² + ( 21)² - 2*13*21*cos ( 120)

c = 29.715 units

from law of sine:

sin A / a = sin B/b = sin C/c

from sin A/ a = sin C/c

sin A = ( a/c)* sin C

sin A = ( 21 / 29.715) * sin ( 120)

sin A = 0.6120

A = sin^-1 ( 0.6120) = 37.7 degree

B = 180 - A - C

B = 180 - 37.7 - 120 = 22.3 degree

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2) let b = 12

a = 40

c = 41

from law of cosine:

cos C = a² + b² - c² / 2*a*b

= 40² + 12² - 41² / ( 2*40*12)

cos C = 0.0656

C = 86.2 degree

cos A = b² + c² - a² / 2*b*c

= 12² + 41² - 40² / ( 2*12*41)

cos A = 0.2286

A = 76.8 degree

B = 180 - 86.2 - 76.8 = 17.0 degree