Answer: BC = 5.3
===============================================
Step-by-step explanation:
Side AB is opposite angle C.
Convention is that the lowercase letters represent the side lengths, and they are opposite the uppercase angles.
- Angle A is opposite side 'a'
- Angle B is opposite side 'b'
- Angle C is opposite side 'c'
In short, side AB can be relabeled as side c. Therefore, c = 6.
Angle BAC can be shortened to simply saying angle A.
Angle ABC is shortened to angle B.
The angle names are drawn directly from the middle letter.
------------------
Here's the given info:
- side c = 6
- angle A = 50
- angle B = 70
Let's use the idea that all 3 angles of a triangle must add to 180 to find angle C.
A+B+C = 180
C = 180-A-B
C = 180-50-70
C = 60
Now let's use the law of sines to determine side 'a'.
a/sin(A) = c/sin(C)
a/sin(50) = 6/sin(60)
a = sin(50)*6/sin(60)
a = 5.3073115853515 approximately
a = 5.3 after rounding to one decimal place
Segment BC is approximately 5.3 cm long.