Some Applicatio...

Two poles are $$10\ m$$ and $$20\,m$$ high. The line joining their tops makes an angle of $$15^\circ$$ with the horizontal. The distance between the poles is approximately equal to

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $${60}^{o}$$, when he retires $$40m$$ from the bank he finds the angle to $${30}^{o}$$. The breadth of river is

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

The base of a cliff is circular. From the extremities of a diameter of the base, angles of elevation of the top of the cliff are $${ 30 }^{ \circ }$$ and $${ 60 }^{ \circ }$$. If the height of the cliff be $$500 \text{ m}$$, then the diameter of the base of the cliff is

A kite is flying with the string inclined at $${75}^{o}$$ to the horizon. If the length of the string is $$25 m$$, then height of the kite is :

From the top of a tower, the angle of depression of a point on the ground is $$60^o$$ . If the distance of this point from the tower is $$ \dfrac {1}{\sqrt{3}+1}$$ m, then the height of the tower is :

The angle of elevation of the top of a tower at a point on the ground is $$30^o$$. If on walking 20 m toward the tower, the angle of elevation becomes $$60^o$$, then the height of the tower is:

A vertical pole $$PS$$ has two marks at $$Q$$ and $$R$$ such that the portions $$PQ, PR$$ and $$PS$$ subtend angles $$\alpha, \beta$$ and $$\gamma$$ at a point on the ground distance $$x$$ from the bottom of pole. If $$PQ = a, PR = b, PS = c$$ and  $$\alpha + \beta + \gamma = 180^{\circ}$$ then $$x^{2}$$ is equal to

The length of the shadows of a vertical pole of height $$h$$, thrown by the sun's rays at three different moments are $$h$$, $$2h$$ and $$3h$$. The sum of the angles of elevation of the rays at these three moments is equal to

The angle of elevation of the top of a tower from the top of a house is $${ 60 }^{ \circ }$$ and the angle of depression of its base is $${ 30 }^{ \circ }$$. If the horizontal distance between the house and the tower be $$12\ m$$, then the height of the tower is