Mathematics 4024 · O Level · Non-right-angled triangles

Non-right-angled triangles — practice question

$ABCD$ is the sloping rectangular face of the triangular prism. $ABEF$ forms a horizontal rectangle, and $EC$ and $DF$ are vertical. $\angle CBE = 15^\circ$, $DC = 5\text{ m}$ and $AD = 2\text{ m}$.
(a(i))[2]

Calculate the length of $AC$.

(a(ii))[2]

Calculate the value of $CE$.

(a(iii))[4]

Calculate the value of $\angle F\hat AE$.

(b(i))[3]

A triangle has side lengths of $10\text{ cm}$, $9\text{ cm}$ and $6\text{ cm}$, together with an angle of $\theta^\circ$, as shown in the diagram. Calculate $\theta$.

(b(ii))[1]

In triangle $KGH$, the side lengths are $a\text{ cm}$, $b\text{ cm}$ and $c\text{ cm}$. You are told that $\angle KGH$ is obtuse. Complete the statement below by choosing one of the symbols $<$, $\le$, $=$, $\ge$, $>$. $c^2 \; ..... \; (a^2 + b^2)$.

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