Let a =107° and b=42°;
So cos 107° cos 42° + sin 107° sin 42° = cosa.cos42 + sina.sinb = cos(a-b)
and cos 107° cos 42° + sin 107° sin 42° = cos(107-42) = cos(65°)
The answer is
AB = 6.
External value x (external value + internal value) =
External value x (external value + internal value) of the other side
Substitute, transpose, and simplify.
TA x (TA + AB) = TC x (TC + CD)
10 x (10 + (x + 2)) = 8 x (8 + 12)
120 + 10x = 160
10x = 40
x = 4
To find AB: x + 12; x = 4
AB = x + 2
AB = 4 + 2
AB = 6
I always found it easiest to draw out the picture
A(b)+16 = 16 larger than the product of a and b.