Alvin has a crate in the shape of a cuboid - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

To find the angle that the stick makes with the base of the crate, we can use trigonometry. Specifically, we will use the tangent function:

Given that the length of the stick above the crate is 40 cm (from part (a)) and the height of the crate is 55 cm, we can use the following relationship:

$tan( heta) = \frac{opposite}{adjacent}$

Here, the "opposite" side is the height of the crate (55 cm), and the "adjacent" side is the length of the stick above the crate (40 cm). Therefore:

$tan( heta) = \frac{55}{40}$

To find the angle, we take the arctangent (inverse tangent):

$\theta = arctan\left(\frac{55}{40}\right)$

Calculating this gives:

$\theta \approx 40.2°$

Thus, the angle the stick makes with the base of the crate is approximately 40.2°.