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

The correct option is A.

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=(BD)/(AB)`

`AB\sin A=BD`

Area of the triangle is

`A=(1)/(2)* base* height`

`A=(1)/(2)* (AC)* (BD)`

`A=(1)/(2)* (AC)* (AB)\sin A`

`A=(1)/(2)(AC)(AB)\sin A`

Therefore option A is correct.