Question

Which equation represents the area of ΔABC?

A) A = 1/2 bc(sin A)
B) A = 1/2 ba(sin A)
C) A = 1/2 ac(sin A)
D) A = 1/2 hc(sin A)

Answer 1

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

Answer 2

Heres a shorter version for the fast paced ones.

1. CD

2. CD/b

3. 1/2bcsin(A)

Explanation:

I just took the test on edge