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

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, \(\tan{\angle ABC}=\tan{\angle DEC} \).

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