Some Applicatio...

The angles of elevation of the top from two points on either side of a tree are $$30^{\circ}$$ and $$60^{\circ}$$. Find the height of the tree if the two points are $$52\ m$$ apart.

The height of a tower is 'h' and $$\alpha$$ is the angle of elevation of the top of the tower. On moving a distance $$\dfrac {h}{2}$$ towards the tower, the angle of elevation becomes $$\beta$$. What is the value of $$\cot \alpha - \cot \beta$$?

A pole is $$20$$ feet high. A taut wire that is $$46$$ feet extends from the top of the pole to the ground. What is the angle of depression, to the nearest degree, from the top of the pole to the bottom of the wire?

The angle of elevation of a ladder leaning against a wall is $$60^{\circ}$$ and the foot of the ladder is $$4.6\ m$$ away from the wall. The length of the ladder is:

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of $$30^{\circ}$$ with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes $$60^{\circ}$$. What is the distance between the base of the tower and the point P?

The angle of depressions of the tap and the foot of a chimney as seen from the top of a second chimney, which is 150 m high and standing on the same level as the first are $$\theta$$ and $$\phi$$ respectively then the distance between their tops when $$tan\, \theta =\frac{4}{3}\,\,and\,\, tan\, \phi =\frac{5}{2}$$ is.

An observer from the top of the light house, the angle of depression of two ships $$P$$ and $$Q$$ anchored in the sea to the same side are found to have measure $$35$$ and $$50$$ respectively. Then from the light house ...............

From the top of a building $$h$$ metre high, the angle of depression of an object on the ground has a measure $$\theta$$. The distance of the object from the building is

On walking ............... metres on a slope at an angle of measure 30 with the ground, one can reach the height '$$a$$' metres from the ground.

When observed from top of a tower, the angle of depression of two houses $$A$$ and $$B$$ in the eastern and western directions is $${30}^{o}$$ and $${60}^{o}$$ respectively, then