The length of the shadow of a pole inclined at $10^\circ$ to the vertical towards the sun is $2.05 \text{ m}$,when the elevation of the sun is $38^\circ$. The length of the pole is

$A$ house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is $60^\circ$. If the distance between the two houses is $6 \ m$,then the height of the first house is:

$A$ vertical pole fixed to the horizontal ground is divided in the ratio $3:7$ by a mark on it,with the lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground $18 \ m$ away from the base of the pole,then the height of the pole (in $meters$) is:

$A$ person standing on the top of a building of height $60 \sqrt{3}$ feet observed the top of a tower to lie at an elevation of $45^{\circ}$. That person descended to the bottom of the building and found that the top of the same tower is now at an angle of elevation of $60^{\circ}$. The height of the tower (in feet) is

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be $45^{\circ}$. After walking a distance of $80 \ m$ towards the top,up a slope inclined at an angle of $30^{\circ}$ to the horizontal plane,the angle of elevation of the top of the hill becomes $75^{\circ}$. Then the height of the hill (in meters) is

$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$, all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to: