Answer: Here is an example, and you can plug your own numbers into the equations and solve.
law of sines is:
a/sin(A) = b/sin(B) = c/sin(C)
you have:
a = 70m
b = 31m
A = 115 degrees.
the part of the law can use is:
a/sin(A) = b/sin(B)
this equation becomes:
70/sin(115) = 31/sin(B)
multiply both sides of this equation by sin(115) and multiply both sides of this equation by sin(B) and you get:
70 * sin(B) = 31 * sin(115)
this is the same thing you would do if i told you to cross multiply.
now divide both sides of the equation by 70 to get:
sin(B) = (31 * sin(115) / 70
use your calculator to solve for sin(B) to get:
sin(B) = (31 * .906307787) / 70 which becomes:
sin(B) = 28.0955414 / 70 which becomes:
sin(B) = .401364877
use your calculator to solve for B to get:
B = arc sin(.401364877) = 23.6635313 degrees.
confirm by plugging into your original equation to get:
a/sin(A) = b/sin(B) becomes:
31/.401364877 = 70/.906307787 which becomes:
77.23645433 = 77.23645433, confirming the answer for angle B is good.
your answer is:
A = 23.6635313 degrees
you now have:
a = 70m
b = 31m
A = 115 degrees.
B = 23.6635313 degrees.
C = 180 - A - B = 41.3364687
this is because the sum of the angles of a triangle must be equal to 180 degrees.
you can use the law of sines again to solve for c.
you can use either:
a/sin(A) = c/sin(C)
or you can use:
b/sin(B) = c/sin(C)
either one will get you the answer.
using b/sin(B) = c/sin(C), we get:
31/sin(23.6635313) = c/sin(41.3364687), we get:
c = (31 * sin(41.3364687))/sin(23.6635313) which gets:
c = 51.0131112
you now have:
a = 70m
b = 31m
c = 51.0131112
A = 115 degrees.
B = 23.6635313 degrees.
C = 41.3364687
confirm the answer is correct by taking any angle and deriving the common ratio.
take a/sin(A) to derive k = 77.23645433
if all is good, then:
b/k = sin(B) which makes B = 23.6635313
c/k = sin(C) which makes C = 41.3364687
