$$\text{Note: Figure not drawn to scale}$$

In the figure above, $ABC$ and $DEC$ are right triangles. If $CD=15$ and the tangent of angle $ABC$ is 1.5, what is the length of segment $ED$?

Summary Submit

We should first note that $\triangle ABC \sim \triangle DEC$ because they share $\angle C$ and each have a right angle (SS similarity). Therefore, $\tan{\angle ABC}=\tan{\angle DEC}$.

$$\tan{\angle ABC}=\tan{\angle DEC}$$ $$1.5 = \frac{\overline{CD}}{\overline{ED}}$$ $$1.5 = \frac{15}{\overline{ED}}$$ $$\overline{ED}= \frac{15}{1.5}$$ $$\overline{ED}=\boxed{10}$$