Question

if wu = 14, uv = 10, and xy = 14, find the length of (overline{zx}). round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Check triangle similarity

Triangles WUV and ZYX have angles 42°, 49°, 89° (AA similarity).

Step2: Identify corresponding sides

WU (opposite 89° in WUV) ↔ ZX (opposite 89° in ZYX); UV (opposite 49° in WUV) ↔ XY (opposite 49° in ZYX).

Step3: Set up proportion

$\frac{WU}{ZX} = \frac{UV}{XY}$

Step4: Solve for ZX

$\frac{14}{ZX} = \frac{10}{14} \implies ZX = \frac{14 \times 14}{10} = 19.6$

Answer:

19.6