Solve the triangle ABC with a=123,b=224,c=28minutes and 40 seconds?

1 Answer
Mar 24, 2018

#color(blue)("side " c = 101),color(red)( "Area of triangle " A_t = 114.21 " sq units"#

Explanation:

https://www.slideshare.net/nsimmons/11x1-t04-05-sine-rule-2011

#"Given : " a = 123, b = 224, hatC = 28' 30 sec#

First let's convert #hatC# into degrees.

60" = 1' , #60' = 1^@#, 3600" = #1@#

#:. 0^@ 28' 30#" = #0 + 28/60 + 30/3600 = 0.475^@#

Area of triangle #A_t = (1/2) a b sin C#

#A_t = (1/2) * 123 * 224 * sin (0.475^@) = color(red)(114.21 " sq units"#

Third side c can be obtained by using Law of Cosines

http://www.mathwarehouse.com/trigonometry/law-of-cosines-formula-examples.php

#c^2 = a^2 + b^2 - 2 a b cos C#

#c^2 = 123^2 + 224^2 - 2 * 123 * 224 * cos (0.475^@)#

#c^2 = 10202.89#

#color(blue)("side " c = 101 " units"#