Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale. (there are two triangles: one labeled w, v, u with angles 88°, 38°, 54° and sides 6, 10; the other labeled with angle 38° at the top, angle 88° at z, angle 54° at x, side 30 and side x to solve for.)

Explanation:

Step1: 确定相似三角形

观察两个三角形的角，\(\triangle WUV\)和\(\triangle ZX\)（设顶点为\(Y\)）的角分别为\(88^\circ\)、\(54^\circ\)、\(38^\circ\)，所以两个三角形相似（AA相似判定）。

Step2: 应用相似三角形比例

在相似三角形中，对应边成比例。\(\triangle WUV\)中边\(WU = 6\)，\(UV = 10\)；\(\triangle ZYX\)中边\(YX = 30\)，\(ZX = x\)。对应边比例为\(\frac{WU}{ZX}=\frac{UV}{YX}\)，即\(\frac{6}{x}=\frac{10}{30}\)。

Step3: 求解\(x\)

交叉相乘得\(10x = 6\times30\)，即\(10x = 180\)，两边除以\(10\)得\(x = 18.0\)。

Answer:

\(18.0\)