Question

2 triangle abc is shown. the lengths of the sides of the triangle are represented by a, b, and c. select the next step that is needed to derive the equation for the area of triangle abc when sides bc, ac, and the included step 1: ( a = \frac{1}{2}bh ) step 2: ( sin c = \frac{h}{a} ) step 3: ( \boldsymbol{
abla} ) step 4: ( a = \frac{1}{2}ab cdot sin c )

Explanation:

Step1: Solve for h from Step2

From $\sin C = \frac{h}{a}$, multiply both sides by $a$: $h = a \cdot \sin C$

Step2: Substitute h into Step1

Substitute $h = a \cdot \sin C$ into $A = \frac{1}{2}bh$: $A = \frac{1}{2}ab \cdot \sin C$ (matches Step4)

Answer:

$h = a \cdot \sin C$