Answer:
Explanation:
Triangle 1 given: 100° , 17 yds, 30 yds
Triangle 2 given: 30 ,17,18
law of cosines: c^2 = a^2 + b^2 − 2ab cos(C)
we'll also need the formula for a SSS triangle
Cos(C) = a^2 + b^2 - c^2 / 2ab
keeping the above in mind we can now solve both triangles
c = AC for the first triangle
solve law of cosines for what we know
c^2= 17^2 + 30^2 - 2*17*30*Cos(100)
c = 36.96
now use SSS triangle formula to find the angle C, but c = 17 now , not 36.96, that's b
C = arcCos(17^2+36.96^2-30^2/ 2*17*36.96)
C = 42.24°
now use 180 = 100 +42.24 +A to solve the last angle
A= 37.75°
Triangle 1 solved
A= 37.75°
B= 100
C = 42.24°
a= 17
b=30
c=36.96
Triangle 2
given a=17 , b= 18 , c =30
use SSS formula to find one angle, which ever one you want in this case
Cos(C) = a^2 + b^2 - c^2 / 2ab
C = arcCos(17^2+18^2-30^2 / 2*17*18
C= 117.966°
solve for A now
Cos(A) =b^2+c^2-a^2 / 2bc
A = arcCos(18^2+30^2-17^2/2*18*30)
A = 30.03
use 180 again to solve for last angle
180 = 117.966+30.03+B
32.001 = B
Triangle 2 solved
A = 30.03°
B= 32.001°
C= 117.966°
a=17
b=18
c=30
:P whew