Take the formula for the area of a triangle, whose base measures b and its corresponding height measures h. So, the area of ABC is
b · h
Area = ———— (i)
2
There is also a right triangle in the picture, in which h is the length of the opposite leg to the angle Â, and c is the length of the hypotenuse. So, you can compute the sine of Â:
length of the opposite side to Â
sin  = ——————————————————
length of the hypotenuse
h
sin  = ——
c
Then,
h = c · sin  (ii)
Now, substitute that into (i) for h, and you get
b · (c · sin Â)
Area = ————————
2
1
∴ Area = —— bc · sin  ✔
2
Answer: option A) A = 1/2 bc sin Â.
I hope this helps. =)
Tags: triangle area length base height sine sin internal angle trigonometry plane geometry
