To calculate the length $d$ using the sine rule, we can apply:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Here, we have:

• $a = d$, $A = 42^\circ$
• $b = 36.5 \, \text{m}$, $B = 67^\circ$

Applying the sine rule:

$\frac{d}{\sin 42^\circ} = \frac{36.5}{\sin 67^\circ}$

Solving for $d$:

$d = \frac{36.5 \cdot \sin 42^\circ}{\sin 67^\circ}$

Calculate this using a calculator:

1. $\sin 42^\circ \approx 0.6691$
2. $\sin 67^\circ \approx 0.9205$

$d = \frac{36.5 \times 0.6691}{0.9205} \approx \frac{24.42915}{0.9205} \approx 26.54 \, \text{m}$

So, the length $d$ is approximately $26.54 \, \text{m}$ to 2 decimal places.