Question

In the following figure, DXS and XZS are right triangle, with right angles Z and D, and SX is the bisector of angle DXZ. Which is the ratio of DX to ZS? In the following figure, DXS and XZS are right triangle, with right angles Z and D, and SX is the bisector of angle DXZ. Which is the ratio of DX to ZS? @Mathematics

Answer 1

\[\frac{\text{DX}}{\text{ZS}}=\frac{9}{\sqrt{15^2-9^2}}=\frac{3}{4} \]

Answer 2

A trig solution:\[\frac{\text{DX}}{\text{ZS}}==\frac{9}{9\text{Cot}\left[\text{ArcSin}\left[\frac{9}{15}\right]\right]}\text{=}\frac{3}{4}\]