# Math Help - I need help with a math proof

1. ## I need help with a math proof

have to prove these two formulas are equal...

Area of a triangle= 1/2 bc sinA

Area of a triangle= 1/2 bh

2. Hello, its.all.up.2.u!

Prove: $\text{Area of a triangle} \:=\:\tfrac{1}{2}bc \sin A$
Code:
            B
*
*| *
c  * |   *   a
*  |h    *
*   |       *
*    |         *
A *  *  *  *  *  *  * C
b

We know that the area is: . $\text{Area} \:=\:\tfrac{1}{2}\text{(base)(height)}$ .[1]

The base of the triangle is side $b.$ .[2]

In the right triangle at the left: . $\sin A \,=\,\frac{h}{c} \quad\Rightarrow\quad h \,=\,c\sin A$ .[3]

Substitute [2] and [3] into [1]:

. . . $\text{Area} \:=\:\tfrac{1}{2}\underbrace{\text{(base)}}_{b} \underbrace{\text{(height)}}_{c\sin A} \;=\;\tfrac{1}{2}bc\sin A$