Taylor designs a logo using isosceles triangles joined at a central point, P - OCR - GCSE Maths - Question 8 - 2023 - Paper 6

To find the height, h, of an isosceles triangle with the base b, we can use the properties of the triangle and trigonometry.

Given that the rotational symmetry has order 60, each triangle subtends an angle of:

$\theta = \frac{360°}{60} = 6°$

Since the triangles are isosceles, we can note that the height h bisects the base b, meaning that:

$\frac{b}{2} = \frac{40}{2} = 20 mm$

Using the tangent function:

$\tan(\theta/2) = \frac{h}{\frac{b}{2}} \Rightarrow \tan(3°) = \frac{h}{20}$

Thus, we can rearrange to find h:

$h = 20 \cdot \tan(3°)$

Now, using a calculator:

$h \approx 20 \cdot 0.0524 \approx 1.048$

Rounding to one decimal place, we find that:

$h \approx 1.0 mm$