Mathematics 4024 · O Level · Pythagoras' theorem and trigonometry in 3D
Pythagoras' theorem and trigonometry in 3D — practice question
A vertical mast, $XY$, stands on horizontal ground. Four cables hold the mast, each fixed to the mast at $P$ and to the ground at points $A$, $B$, $C$ and $D$. $Y$ is the centre of square $ABCD$. $PY = 7.50\text{ m}$.
(a)[3]
Show that $AY = 2.58\text{ m}$ correct to $3$ significant figures, given that $AB = 3.65\text{ m}$.
(b)[2]
Calculate the length of one cable that supports the mast.
(c)[3]
Calculate the value of $\angle APB$.
(d(i))[2]
From $A$, the angle of elevation of $X$ is $77.0^\circ$. Calculate the height, $XY$, of the mast.
(d(ii))[2]
Calculate the angle of elevation of $X$ from the midpoint of $AB$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Trigonometry or Pythagoras” …