Some Applicatio...

An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt {3}\ km$$ above it, is observed at an elevation of $$60^{o}$$ from a point on the ground. If, after five seconds, its elevation from the same point, is $$30^{o}$$, then the speed (in $$km/ hr$$) of the aeroplane, is

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of $$60^{\circ}$$ at the foot of the tower, and the angle of elevation of the top of the tower from A or B is $$30^{\circ}$$. The height of the tower is

A bird is sitting on the top of a vertical pole $$20$$ m high and its elevation from a point $$O$$ on the ground is $$ 45^{\circ}$$. It flies off horizontally straight away from the point $$O$$. After one second, the elevation of the bird from $$O$$ is reduced to $$ 30^{\circ}$$. Then the speed (in $$m/s$$) of the bird is

Let $$10$$ vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $$\alpha$$ at a point $$O$$ on this line and all the poles are on the same side of $$O$$. If the height of the longest pole is $$h$$ and the distance of the foot of the smallest pole from $$O$$ is $$a$$; then the distance between two consecutive poles, is

$$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. A man finds that the angle of elevation of the point A from a certain point $$C$$ on the ground is $$60^{{o}}$$. He moves away from the pole along the line $$BC$$ to a point $$D$$ such that $$CD=7$$ m. From $$D$$ the angle of elevation of the point $$A$$ is $$45^{{o}}$$. Then the height of the pole is 

A tower $$T_{1}$$ of height $$60\ m$$ is located exactly opposite to a tower $$T_{2}$$ of height $$80\ m$$ on a straight road. From the top of $$T_{2}$$, if the angle of depression of the foot of $$T_{1}$$ is twice the angle of elevation of the top of $$T_{2}$$ from top of $$T_1,$$ then find the width of the road between the feet of the towers $$T_{1}$$ and $$T_{2}$$.$$\left(\text{Use  }\tan 2\theta  = \dfrac{{2\tan \theta }}{{1 - {{\tan }^2}\theta }}\right)$$

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point $$A$$ on the path, he observes that the angle of elevation of the top of the pillar is $$\displaystyle { 30 }^{ \circ  }$$. After walking for $$10$$ minutes from $$A$$ in the same direction, at a point $$B,$$ he observes that the angle of elevation of the top of the pillar is $$\displaystyle { 60 }^{ \circ  }$$. Then the time taken (in minutes) by him, from $$B$$ to reach the pillar is:

$$PQR$$ is a triangular park with $$PQ = PR = 200\ m$$. A T.V. tower stands at the mid-point of $$QR$$. If the angles of elevation of the top of the tower at $$P, Q$$ and $$R$$ are respectively $$45^{\circ}, 30^{\circ}$$ and $$30^{\circ}$$, then the height of the tower (in $$m$$) is

A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of $$\displaystyle { 60 }^{ \circ  }$$ with the horizontal and height of the house be $$\displaystyle 6\sqrt { 3 } \text{ m}$$, then the length of the ladder is:

A kite is flying at an inclination of $$60^\circ$$ with the horizontal. If the length of the thread is $$120\text{ m},$$ then the height at which kite is: