How do you solve a triangle if you are given a=2.5, b=10.2, c=9?

1 Answer
Jul 8, 2015

Answer:

#/_A = 0.229406# radians
#/_B = 1.953156# radians
#/_C = 0.959031# radians

Explanation:

For a triangle with
#color(white)("XXXX")#side #a# opposite angle #A#
#color(white)("XXXX")#side #b# opposite angle #B#
#color(white)("XXXX")#side #c# opposite angle #C#
The Law of Cosines says:
#color(white)("XXXX")##c^2 = a^2+b^2-2abcos(C)#
or
#color(white)("XXXX")##cos(C) = (a^2+b^2-c^2)/(2ab)#
#color(white)("XXXX")##color(white)("XXXX")#(and similarly for #A# and #B#)

So
#color(white)("XXXX")##cos(C) = (2.5^2+10.2^2-9^2)/(2(2.5)(10.2))#

#color(white)("XXXX")##color(white)("XXXX")##=0.574314#

#C = "arccos"(cos(C))#
#color(white)("XXXX")##C = "arccos"(0.574314)#
#color(white)("XXXX")##color(white)("XXXX")##=0.959031# radians
#color(white)("XXXX")##color(white)("XXXX")#(using a calculator)

Similar calculations can be made for angles #A# and #B#