Answer:
3.4 inches
Explanation:
You want the length of side o in ∆MNO with N = 52°, O = 23°, and m = 8.5 inches.
Law of Sines
The law of sines tells you the side lengths of a triangle are proportional to the sine of the opposite angle:
o/sin(O) = m/sin(M)
In order to make use of this relationship, we need the value of angle M.
M +N +O = 180°
M =52° +23° = 180°
M = 105° . . . . . . . . . . subtract 75°
Now, we can find the length o:
o = m·sin(O)/sin(M) = (8.5 in)·sin(23°)/sin(105°) ≈ 3.4384 in
The length of o is about 3.4 inches.