Higher November 2020 Unit 2 Q6
6. In the diagram below, AB, BC and CD are three sides of a regular polygon.
The polygon has 15 sides.
The length of each side is 8 cm.
The exterior angle of the polygon is \(x^\circ\).
BRC is a right-angled triangle.
Diagram not drawn to scale
Calculate the length of BR. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \((x =)\ \dfrac{360}{15}\) or \(180 - \dfrac{(15 - 2)\text{ x }180}{15}\) or equivalent | M1 | May be seen in parts. |
| \(= 24(^\circ)\) | A1 | |
| \((BR =)\ 8 \times \cos 24\) or \(8 \times \sin (90 - 24)\) | M2 | FT ‘their stated value for \(x\)’ (\(x \lt 90^\circ\)) M1 for \(\dfrac{BR}{8} = \cos 24\) or \(\dfrac{BR}{8} = \sin (90 - 24)\) Accept equivalent of using sin rule (as sin 90 = 1). |
| = 7·3(0…)(cm) or 7·31(cm) | A1 |
Alternative method to find BR
| Scheme | Marks | Comments |
|---|---|---|
| A correct and complete method (using two trigonometric relationships and possibly Pythagoras’s theorem) | M2 | |
| BR = 7·3(0…)(cm) or 7·31(cm) | A1 |