Question

find df
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df =

Explanation:

Step1: Determine similar triangles

Since $\angle A = \angle D=36^{\circ}$ and in $\triangle ABC$, $\angle B=180^{\circ}-36^{\circ}-26^{\circ}=118^{\circ}=\angle E$, the two triangles $\triangle ABC$ and $\triangle DEF$ are similar.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. Let's assume the ratio of corresponding sides of $\triangle ABC$ and $\triangle DEF$ is the same. If we assume the side - length correspondence such that $\frac{AC}{DF}=\frac{BC}{EF}$. We know $AC = 12$, $BC = 8$, $EF = 14$. Let $DF=x$. Then $\frac{12}{x}=\frac{8}{14}$.

Step3: Solve the proportion

Cross - multiply: $8x=12\times14$. So $8x = 168$. Then $x=\frac{168}{8}=21$.

Answer:

21