2019 Nov P2 Q7

Question 7

A landscape artist plans to plant flowers within two concentric circles around a vertical light pole $PQ$ . $R$ is a point on the inner circle and $S$ is a point on the outer circle. $R$ , $Q$ and $S$ lie in the same horizontal plane. $RS$ is a pipe used for the irrigation system in the garden. The radius of the inner circle is $r$ units and the radius of the outer circle is $QS$ . The angle of elevation from $S$ to $P$ is $30^{\circ}$ . $R\hat QS=2x$ and $PQ=\sqrt{3}r$

$7.1$	Show that $QS=3r$	$(3)$
$7.2$	Determine, in terms of $r$ , the area of the flower garden.	$(2)$
$7.3$	Show that $RS=r\sqrt{10-6\cos{2x}}$	$(3)$
$7.4$	If $r=10$ metres and $x=56^{\circ}$ , calculate $RS$ .	$(2)$
		$\textbf{[10]}$

Question 7

The diagram below shows a solar panel,

ABCD

, which is fixed to a flat piece of concrete slab

EFCD

ABCD

and

EFCD

are two identical rhombuses.

K

is a point on

DC

such that

DK=KC

and

AK\perp DC

AF

and

KF

are drawn.

A\hat DC=C\hat DE=60^{\circ}

and

AD=x

units.

7.1

Determine

AK

in terms of

x

(2)

7.2

Write down the size of

K\hat CF

(1)

7.3

It is further given that

A\hat KF

, the angle between the solar panel and the concrete slab, is

y

. Determine the area of

\Delta AKF

in terms of

x

and

y

(7)

\textbf{[10]}

The diagram below shows a solar panel, $ABCD$ , which is fixed to a flat piece of concrete slab $EFCD$ . $ABCD$ and $EFCD$ are two identical rhombuses. $K$ is a point on $DC$ such that $DK=KC$ and $AK\perp DC$ . $AF$ and $KF$ are drawn. $A\hat DC=C\hat DE=60^{\circ}$ and $AD=x$ units.

$7.1$	Determine $AK$ in terms of $x$ .	$(2)$
$7.2$	Write down the size of $K\hat CF$ .	$(1)$
$7.3$	It is further given that $A\hat KF$ , the angle between the solar panel and the concrete slab, is $y$ . Determine the area of $\Delta AKF$ in terms of $x$ and $y$ .	$(7)$
		$\textbf{[10]}$