The angle of elevation of the top $P$ of a vertical tower $P Q$ of height 10 from a point $A$ on the horizontal ground is $45 ^ { \circ }$. Let $R$ be a point on $A Q$ and from a point $B$, vertically above $R$, the angle of elevation of $P$ is $60 ^ { \circ }$. If $\angle B A Q = 30 ^ { \circ } , A B = d$ and the area of the trapezium $P Q R B$ is $\alpha$, then the ordered pair ( $d , \alpha$ ) is (1) $( 10 ( \sqrt { 3 } - 1 ) , 25 )$ (2) $\left( 10 ( \sqrt { 3 } - 1 ) , \frac { 25 } { 2 } \right)$ (3) $( 10 ( \sqrt { 3 } + 1 ) , 25 )$ (4) $\left( 10 ( \sqrt { 3 } + 1 ) , \frac { 25 } { 2 } \right)$
The angle of elevation of the top $P$ of a vertical tower $P Q$ of height 10 from a point $A$ on the horizontal ground is $45 ^ { \circ }$. Let $R$ be a point on $A Q$ and from a point $B$, vertically above $R$, the angle of elevation of $P$ is $60 ^ { \circ }$. If $\angle B A Q = 30 ^ { \circ } , A B = d$ and the area of the trapezium $P Q R B$ is $\alpha$, then the ordered pair ( $d , \alpha$ ) is\\
(1) $( 10 ( \sqrt { 3 } - 1 ) , 25 )$\\
(2) $\left( 10 ( \sqrt { 3 } - 1 ) , \frac { 25 } { 2 } \right)$\\
(3) $( 10 ( \sqrt { 3 } + 1 ) , 25 )$\\
(4) $\left( 10 ( \sqrt { 3 } + 1 ) , \frac { 25 } { 2 } \right)$