Question

Which equation represents the area of ΔABC?

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

Answer:

Heres a shorter version for the fast paced ones.

1. CD

2. CD/b

3. 1/2bcsin(A)

Step-by-step explanation:

I just took the test on edge