Some Applicatio...

A vertical pole stand at a point O on a horizontal ground. A and B are point on the ground 10m apart. The pole subtends an angle 30$$\displaystyle ^{\circ}$$ and 60$$\displaystyle ^{\circ}$$ at A and B, respectively, and AB subtends an angle 45$$\displaystyle ^{\circ}$$ at O. Then height of tower equals 

A man on a cliff observes a boat at an angle of depression of $$\displaystyle 30^{\circ} $$ which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later the angle of depression of the boat is found to be $$\displaystyle 60^{\circ}. $$ Find the total time taken by the boat from the initial point to reach the shore.

The angle of elevation of the top of tower as observed from a pint on the horizontal ground is 'x' if we move a distance 'd' towards the foot of the tower the angle of elevation increases to 'y' then the height of the tower is 

The angle of elevation of the top of a tower as seen from two points $$A$$ & $$B$$ situated in the same line and at distances $$p$$ and $$q$$ respectively from the foot of the tower are complementary then the height of the tower is:

The angle of elevation of the top of a tower at a distance of $$\displaystyle \frac{50\sqrt{3}}{3}$$ metres from the foot is $$\displaystyle 60^{\circ}$$. Find the height of the tower 

If from the top of a tower 50 m high, the angles of depression of two objects due north of the tower are respectively $$\displaystyle 60^{\circ}$$ and $$\displaystyle 45^{\circ}$$, then the approximate distance between the objects is :

The string of a kite $$100$$ metres long and it makes an angle of $$60^{\circ}$$ with the horizontal. Find the height of the kite. 

The length of a ladder is exactly equal to the height of the wall it is leaning against. If the lower end of the ladder is kept on a bench of height 3 m. and the bench is kept 9 m. away from the wall, the upper end of the ladder coincides with the top of the wall. The height of the wall is

The angle of depression of a car moving with uniform speed towards the building as observed from the top of the building is found to be $$30^{\circ}$$. The same angle of depression changes to $$60^{\circ}$$ after $$12$$ seconds. How much more time would the car take to reach the base?

A tower is $$100\sqrt 3 m$$ high. The angle of elevation of its top from a point $$100 m$$ away from its foot is ........