ABCD...FGH is a cuboid - Edexcel - GCSE Maths - Question 19 - 2018 - Paper 2

We can find the length AC using the Pythagorean theorem:
$AC = \sqrt{AB^2 + BC^2} = \sqrt{(7.3)^2 + (7.3)^2} = 7.3 \sqrt{2}$
Thus,
$AC \approx 10.3 cm.$

Using the tangent function:
$\tan(CAH) = \frac{\text{opposite}}{\text{adjacent}} = \frac{CH}{AC} = \frac{8.1}{10.3}$
This gives:
$CAH = \tan^{-1}\left(\frac{8.1}{10.3}\right) \approx 39.5^{\circ}.$

The angle between AH and the plane ABCD, which is denoted as angle CAH, is approximately equal to 39.5°. Thus, the answer rounded to one decimal place is 39.5°.