Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
d
39°
c
86°
97
61
b
55°
f
86°
15
g
39°
x
e
55°

Explanation:

Step1: 确定三角形相似

观察两个三角形，$\triangle DBC$和$\triangle GFE$的三个角分别相等（$\angle D = \angle G = 39^\circ$，$\angle B = \angle E = 55^\circ$，$\angle C = \angle F = 86^\circ$），所以$\triangle DBC \sim \triangle GFE$（AA相似判定）。

Step2: 应用相似三角形的性质

相似三角形对应边成比例，即$\frac{DB}{GF} = \frac{BC}{FE}$。已知$DB = 97$，$BC = 61$，$FE = 15$，设$GF = x$，则$\frac{97}{x} = \frac{61}{15}$。

Step3: 求解$x$

交叉相乘得$61x = 97\times15$，即$61x = 1455$，解得$x = \frac{1455}{61} \approx 23.85$，四舍五入到十分位为$23.9$。

Answer:

$23.9$