Solve ?ABC............................

Question

Solve ΔABC. (Round your answers to the nearest whole number. If there is no solution, enter NO SOLUTION.)

β = 142°,     a = 140,     c = 30

b	=	___
α	=	___ °
γ	=	___ °

Answer 1

Hi Colsten,

 

You can solve this problem using the Laws of Sines and Cosines. The Law of Sines is useful if you know a side and its opposite angle, and one part of the other pairs. The Law of Cosines is useful if you know two sides and their included angle.

 

Law of Sines:

a / sin α = b / sin β = c / sin γ

 

Law of Cosines:

a² = b² + c² - 2bc cos α

b² = a² + c² - 2ac cos β

c² = a² + b² - 2ab cos γ

 

In your problem, you know sides a and c, and the included angle β. You can use the 2nd form of the Law of Cosines to solve for b.

 

b² = 140² + 30² - 2*140*30*cos(142)

 

Once you solve for b, you can use the Law of Sines to solve for α and γ.

 

b / sin β = c / sin γ

(b) / sin (142) = 30 / sin γ

 

a / sin α = b / sin β

140 / sin α = (b) / sin (142)