1.34: Figure 5 shows a right triangular prism where is a rectangle.

4PM1/2/June/2024 — Question 9 · 15 marks

1.34 diagram 1
Figure 5 shows a right triangular prism ABCDEF\displaystyle ABCDEF where ABCD\displaystyle ABCD is a rectangle.
AF=DEBF=CEAD=FE=BCAB=DC=24cmAF = DE \quad BF = CE \quad AD = FE = BC \quad AB = DC = 24 \mathrm{cm}
∠ABF=∠DCE=45∘∠BAF=∠CDE=60∘\angle ABF = \angle DCE = 45^\circ \quad \angle BAF = \angle CDE = 60^\circ
Using a formula from page 2,
(a) show that sinAFB=2+64(a) \text{ show that } \mathrm{sin} AFB = \frac{\sqrt{2} + \sqrt{6}}{4}
(3)
Without using a calculator,
(b) show that BF=12(32−6)cm(b) \text{ show that } BF = 12(3\sqrt{2} - \sqrt{6}) \mathrm{cm}
(5)
The angle between the plane AEB\displaystyle AEB and the plane ABCD\displaystyle ABCD is 65∘\displaystyle 65^\circ
(c) Find, in cm to 2 significant figures, the length of EF(c) \text{ Find, in cm to 2 significant figures, the length of } EF
(3)
(d) Find, in degrees to one decimal place, the size of the angle between the line CF and the plane ABCD(d) \text{ Find, in degrees to one decimal place, the size of the angle between the line } CF \text{ and the plane } ABCD
(4)