Year 12 Methods (Unit 3 & 4)
Trigonometry using the sine and cosine rules
Angles between planes and more complex 3D problems
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Questions
Question 1
194433
A rectangular box \(ABCD\text{-}EFGH\) sits on a horizontal base \(ABCD\), with \(AB=4\text{ cm}\), \(BC=3\text{ cm}\) and vertical height \(CG=12\text{ cm}\). \(AC\) is a diagonal of the base and \(AG\) the space diagonal from \(A\) to \(G\).
(i) Find the length of the base diagonal \(AC\).(ii) Find the length of the space diagonal \(AG\).
(iii) Find the angle \(AG\) makes with the base, to the nearest degree.
Part a:
5
\(\text{ cm}\)
1 mark
Part b:
13
\(\text{ cm}\)
1 mark
Part c:
67
\(^\circ\)
1 mark
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