very good solution !RLBrown said:
The formula for finding the length of $\overline {AD} \times \overline {CD}$ in $\triangle APB$ is $\frac{1}{2} \times \overline {AD} \times \overline {CD} \times sin\angle APB$.
To find the length of $\overline {AD}$ and $\overline {CD}$ in $\triangle APB$, you can use the Pythagorean theorem or trigonometric ratios (such as sine, cosine, or tangent) depending on the information given in the triangle.
The angle $\angle APB$ is essential in finding the length of $\overline {AD} \times \overline {CD}$ in $\triangle APB$ because it is used in the formula for finding the length, as well as in determining which trigonometric ratio to use.
In $\triangle APB$, $\overline {AD}$ and $\overline {CD}$ are the sides that form the right angle, while $\angle APB$ is the angle opposite the hypotenuse, which is typically labeled as $\overline {AB}$.
No, $\overline {AD} \times \overline {CD}$ cannot be negative in $\triangle APB$ because it represents the area of a triangle, and area cannot be negative.
