Answer to Question #223959 in Geometry for ali

Question

The drawing below shows a right-angled triangle. A straight line crosses the triangle parallel to the line z and encloses an angle of α. The lengths x and y of the bottom and top line segments as well as the angle α are given. Find an equation for the length z. 

Answer 1

$\dfrac{x\cos\alpha}{z}=\dfrac{x\sin \alpha}{x\sin \alpha+y}$

$z=(x\sin \alpha+y)\cot\alpha$