The angle of elevation of a ladder leaning against a house is $60^{\circ}$ and the foot of the ladder is $6.5 \ m$ from the house. Find the length of the ladder in metres.

The length of the shadow of a tower is $9 \text{ m}$ when the sun's altitude is $30^{\circ}$. What is the height of the tower? (In $m$)

In a rectangle,if the angle between a diagonal and a side is $30^{\circ}$ and the length of the diagonal is $6 \text{ cm}$,the area (in $\text{cm}^2$) of the rectangle is:

$ABCD$ is a rectangle where the ratio of the lengths of $AB$ and $BC$ is $3:2$. If $P$ is the midpoint of $AB$,then the value of $\sin(\angle CPB)$ is

$A$ tower standing on a horizontal plane subtends a certain angle at a point $160 \; m$ apart from the foot of the tower. On advancing $100 \; m$ towards it,the tower is found to subtend an angle twice as before. The height of the tower is (in $m$):

The angle of elevation of the top of a $TV$ tower from three points $A, B, C$ in a straight line through the foot of the tower are $\alpha, 2 \alpha, 3 \alpha$ respectively. If $AB = a$,the height of the tower is