Some Applicatio...

The angle of elevation of an aeroplane from a point $$30$$ metres above the water level is $$45^{0}$$, and the angle of depression of its reflection in the lake is $$60^{ }$$. The height of the aeroplane above the lake in metres is

A flag staff of height $$(a-b)$$ stands on the top of a tower subtends the same angle at point on the horizontal plane through the foot of the tower which are at distant $$a$$ and $$b$$ form the tower. The height of the tower is

From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be $$\alpha$$ and $$\beta$$. If $$h$$ is the height of the tree, then the height of the tower is:

From the top of cliff $$300\ meters$$ high, the top of tower was observed at an angle of depression $${30}^{\circ}$$ and from the foot of the tower the top of the cliff was observed at an angle of elevation $${45}^{\circ}$$. The height of the tower is

A $$25\ m$$ ladder is placed against a vertical wall of a building. The foot of the ladder is $$7\ m$$ from the base of the building. If the top of the ladder slips $$4\ m$$, then the foot of the ladder will slide by:

A lamp post standing at a point $$A$$ on a circular path of radius $$r$$ subtends an angle $$\alpha$$ at some point $$B$$ on the path, and $$AB$$ subtends an angle of $$45^{\circ}$$ at any other point on the path, the height of the lamp post is

A person walking along a canal observes that two objects are in the same line which is inclined at an angle $$\alpha$$ to the canal. He walks a distance $$C$$ for the and observes that the objects subtended their greatest angle $$\beta$$ then the distance between the object is

Vertical pole $$PO$$ stands at the centre $$O$$ of a square $$ABCD$$. If $$AC$$ subtends an angle at the top $$P$$ of the pole, then the angle $$90^{0}$$ subtended by a side of the square at $$p$$ is

At the foot of a mountain the elevation of its peak is found to be $$\displaystyle \frac{\pi }{4}.$$ After ascending $$ h $$ metres toward the mountain up a slope of $$\displaystyle \frac{\pi }{6}$$ inclination, the elevation is found to be $$\displaystyle \frac{\pi }{3}.$$ Height of the mountain is

The angle of elevation from a point on the bank of a river to the top of a temple on the other bank is $$45^o$$. Retreating $$50\  m$$, the observer finds the new angle of elevation as $$30^{\circ}$$. What is the width of the river ?