4MA0 Higher January 2016 Paper 4R Q21
21 \(ABCDE\) is a square-based pyramid.
Diagram NOT accurately drawn
\(AE = BE = CE = DE = 12\) cm
\(AB = 15\) cm
Calculate the size of angle \(DEB\).
Give your answer to the nearest degree.
(4)
| Scheme | Marks |
|---|---|
(\(BD^2\) or \(AC^2\) =) \(15^2 + 15^2\) or \(\sqrt{450}\) or \(15\sqrt{2}\) or 21.2 ... | M1 |
eg. \(\text{“}\sqrt{450}\text{”}^2 = 12^2 + 12^2 - 2 \times 12 \times 12 \times \cos BED\) or \(\sin BEX = \dfrac{0.5\text{"}\sqrt{450}\text{"}}{12}\) or \(\cos EBD = \dfrac{0.5\text{"}\sqrt{450}\text{"}}{12}\) | M1 |
eg \(DEB = \cos^{-1}\left(\dfrac{12^2 + 12^2 - \text{"}450\text{"}}{2 \times 12 \times 12}\right)\) or \(DEB = 2 \times \sin^{-1}\left(\dfrac{0.5 \times \text{"}\sqrt{450}\text{"}}{12}\right)\) or \(DEB = 180 - 2 \times \cos^{-1}\left(\dfrac{0.5 \times \text{"}\sqrt{450}\text{"}}{12}\right)\) or \(DEB = 55.7\ldots\) or 56° (from ambiguous case of Sine Rule) | M1 |
| 124 | A1 |
| (4) |
Notes
M1: A correct statement to find diagonal of base
M1: dep
for use of cosine rule – correct statement in any form or correct trig statement to find angle \(BED\) or angle \(BEX\) or angle \(EBD\) or angle \(EDB\)
NB: Any multi-step method must be fully correct
M1: Complete correct method to find angle \(DEB\)
A1: answer in range 124 – 124.3