A stand is being used to prop up a portable solar panel - Leaving Cert Mathematics - Question 8 - 2014

To find the length of the strap [DE], we first need to calculate the length of segment |DC|. Since |AB| = 30 cm and |AD| = 5 cm, we have:

$|DC| = |AB| - |AD| = 30 cm - 5 cm = 25 cm$

Next, we will use the Sine Rule in triangle ΔACF considering α = 60°:

$\frac{\sin(60°)}{|CF|} = \frac{\sin(|LF|)}{|AC|}$

Given that |CF| = 22 cm and |AC| = 25 cm, we have:

$\sin(|LF|) = \frac{22 \sin(60°)}{25}$

Now evaluating this gives:

$|LF| = \sin^{-1}(0.9841)\approx 79.77°$

Now we need to calculate the angle |LC|:

$|LC| = 180° - 79.77° - 60° = 40.23°$

Next, we will use the Cosine Rule for triangle ΔCDE:

$|DE|^2 = |DC|^2 + |CE|^2 - 2|DC||CE| \cos(40.23°$

Substituting the lengths into the equation:

$|DE|^2 = 20^2 + 18^2 - 2(20)(18)\cos(40.23°) \approx 174.3$

Therefore,

$|DE| = \sqrt{174.3} \approx 13.20 cm$