To calculate the length of $AC$, we first need to analyze the given information in the diagram.

Here's what we know from the image:

1. $AB$ is perpendicular to $BC$.
2. $BD$ bisects the angle at point $D$ with $\angle DAB = 53^\circ$ and $\angle DBC = 67^\circ$.
3. $BC = 91 \, \text{m}$.

We need to find the length of $AC$.

Steps to Solve:

1. Identify triangles involved: The triangles involved are $\triangle ABD$ and $\triangle BCD$.

2. Use trigonometric ratios: Since $\angle DAB = 53^\circ$ and $\angle DBC = 67^\circ$, and considering that $BD$ is a straight line bisecting $D$, we can use the trigonometric ratios to find $AB$ and $BC$.

3. Calculate $AB$ using trigonometry: In $\triangle BCD$: $\tan(67^\circ) = \frac{BD}{BC}$ So, $BD = BC \cdot \tan(67^\circ)$ Since $BC = 91 \, \text{m}$, $BD = 91 \cdot \tan(67^\circ)$

4. Calculate $AC$: To find $AC$, we can use the cosine law or extend further using trigonometry. However, once we have $BD$ and $BC$ the lengths of sides complete required remain.

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