Question

Which equation represents the area of the triangle? A) A = 1 2 (AC)(AB)(sin A) B) A = 1 2 (AC)(BC)(sin A) C) A = 1 2 (BC)(BD)(sin A) D) A = 1 2 (AB)(BD)(sin A) Eliminate

Answer 1

Answer:

The correct option is A.

Step-by-step explanation:

Let the vertices of the triangle be ABC.

Draw a perpendicular on AC from B. The height of triangle is represented by the altitude from B.

$\sin A=\frac{BD}{AB}$

$AB\sin A=BD$

Area of the triangle is

$A=\frac{1}{2}\times base\times height$

$A=\frac{1}{2}\times (AC)\times (BD)$

$A=\frac{1}{2}\times (AC)\times (AB)\sin A$

$A=\frac{1}{2}(AC)(AB)\sin A$

Therefore option A is correct.