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

To find the angle, we can use the height of the crate and the length of the stick. The relationship involves the tangent function:

$an( heta) = \frac{\text{opposite}}{\text{adjacent}}$

Here, the opposite side is the height of the crate (55 cm) and the adjacent side is the length that remains in the crate, which we can calculate as:

Length in crate = Length of stick - Length extending out = 95 ext{ cm} - 40 ext{ cm} = 55 ext{ cm}

Then we can write:

$an( heta) = \frac{55 ext{ cm}}{\sqrt{(40 ext{ cm})^2 + (55 ext{ cm})^2}}$

Using the Pythagorean theorem, the length of the stick in the horizontal direction can be found. After calculations, we can use the inverse tangent function to find the angle:

$heta = \tan^{-1}\left(\frac{55}{40}\right)\approx 40.2^{\circ}$

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