Some Applicatio...

A vertical tower $$CP$$ subtends the same angle $$\theta$$, at point $$B$$ on the horizontal plane through $$C$$, the foot of the tower, and at point $$A$$ in the vertical plane. If the triangle $$ABC$$ is equilateral with length of each side equal to $$4m$$, then height of the tower is:

$$n$$ poles standing at equal distances on a straight road subtend the same angle $$\alpha$$ at a point $$O$$ on the road. If the height of the largest pole is $$h$$ and the distance of the foot of the smallest pole from $$O$$ is $$a$$, the distance between two consecutive poles is:

A $$6$$ ft-tall man finds that the angle of elevation of the top of a $$24$$ ft-high pillar and the angle of depression of its base are complementary angles.The distance of the man from the pillar is

A piece of paper in the shape of a sector of a circle of radius 10cm and of angle $$\displaystyle 216^{\circ}$$ just covers the lateral surface of a right circular cone of vertical angle$$\displaystyle  2\theta$$ .Then $$\displaystyle \sin\: \theta$$ is 

At the foot of the mountain the elevation of its summit is $${ 45 }^{ 0 }$$; after ascending $$1000m$$ towards the mountain up a slope of $${ 30 }^{ 0 }$$ inclination, the elevation is found to be $${ 60 }^{ 0 }$$. The height of the mountain is

A man from the top of a $$100$$-metre-high tower sees a car moving towards the tower at an angle of depression of $$\displaystyle 30^{\circ}$$. After some time, the angle of depression becomes $$\displaystyle 60^{\circ}$$. The distance (in metres) travelled by the car during the time, is

A vertical lamp-post, 6 m high, stands at a distance of 2 m from a wall, 4 m high. A 1.5-m-tall man starts to walk away from the wall on the other side of the wall, in line with the lamp-post.The maximum distance to which the man can walk remaining in the shadow is 

The angle of elevation of the top of a vertical pole when observed from each vertex of a regular hexagon is$$\displaystyle \frac{\pi}3$$. If the area of the circle circumscribing the hexagon be $$A\ \displaystyle m^{2},$$ then the area of the hexagon is

$$AB$$ is a vertical pole with base at $$B$$. A man finds the angle of elevation of the point $$A$$ from a certain point $$C$$ on the ground is $$60^{0}$$ . He move away from the pole along line $$BC$$ to a point $$D$$ such that $$CD= 7\:m$$ , from $$D$$ the angle of elevation of point $$A$$ is $$45^{0}$$ , then height of the pole is

At the foot of the mountain the elevation of its summit is $${45}^{0}$$; after ascending $$1000\ m$$ towards the mountain up a slope of $${30}^{0}$$ inclination, the elevation is found to be $${60}^{0}$$. The height of the mountain is