If a, b and c are all acute angles in a triangle and sinA = m and sinB = n, find sin c in terms of m and n?
I do not understand how to do this one, please help!
I do not understand how to do this one, please help!
1 Answer
May 3, 2018
Explanation:
Since they are angles of a triangle, we have
So,
Since
In turn,
So far, we only know the sine values, but we don't know the cosines. Using the fundamental relation
(we're taking the positive root because we know that alla angles are between
So, we have:
#sin(a) = m# #cos(a) = sqrt(1-m^2)# #sin(b) = n# #cos(b) = sqrt(1-n^2)#
Plug these values into the formula (1) to get the answer.