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Year 11 (2025) Maths Advanced Trigonometry

Cosine Rule

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Question 1
31098

\(ABCD\) is a parallelogram in which the length of \(AB\) and \(AD\) are 2 cm and 1 cm respectively and \(\angle ABC = 60^\circ\), also the diagonals cut at \(P\) and \(\angle APB = \theta^\circ\).

Calculate the \(\textbf{exact}\) values of

i) \(AC\)

ii) \(BD\)

iii) \(\cos \theta\)

Part a:
A.
\(\sqrt 3\)
Correct
B.
\(\sqrt 7\)
C.
\(\sqrt 5\)
D.
\(3\)
Part b:
A.
\(\sqrt 3\)
B.
\(\sqrt 7\)
Correct
C.
\(\sqrt{13}\)
D.
\(7\)
Part c:
A.
\(\dfrac{\sqrt{21}}{7}\)
B.
\(\dfrac{-\sqrt{21}}{3}\)
C.
\(\dfrac{-\sqrt{21}}{7}\)
Correct
D.
\(-\dfrac{1}{7}\)

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