Question

deriving the trigonometric area formula
follow these steps to derive the trigonometric area formula.

1. for $\triangle abd$, $\sin(a) = \frac{h}{c}$.
2. solve the previous equation for $h$.

$h = c\sin(a)$.

1. use the formula for the area of a triangle, $\text{area} = \frac{1}{2}bh$, and substitute $h$ to get the trigonometric area formula:

$\text{area} = \frac{1}{2}bc\sin(a)$
correct!
check

Explanation:

Step1: Recall substitution goal

We need to replace $h$ in the area formula with the expression from Step 2.

Step2: Substitute $h = c\sin(A)$

Take the basic triangle area formula $\text{area} = \frac{1}{2}bh$, and substitute $h = c\sin(A)$ into it.
$\text{area} = \frac{1}{2}b \times c\sin(A)$

Step3: Simplify the expression

Rearrange the terms in the formula for clarity.
$\text{area} = \frac{1}{2}bc\sin(A)$

Answer:

$\text{area} = \frac{1}{2}bc\sin(A)$