Target Mathematics

1.78: Trigonometric equations and geometry

4PM1/2/June/2017 — Question 10 · 16 marks

1.78 diagram 1
Figure 2 shows a solid cuboid ABCDEFGHABCDEFGH with EF=8EF=8 cm and EH=3EH=3 cm.
The angle between the diagonal AHAH of the cuboid and the plane ABCDABCD is 4545^\circ.
The midpoint of CHCH is NN.
Find, in cm to 3 significant figures,
(a) the length of CHCH, (4)
(b) the length of AHAH, (3)
(c) the length of FNFN. (3)
Find, in degrees to 1 decimal place, the size of
(d) the angle between the plane BCEFBCEF and the plane FGHEFGHE, (3)
(e) angle FNGFNG. (3)