Some Applicatio...

A vertical pole subtends an angle $$\tan^{-1}\dfrac{1}{2}$$ at point $$P$$ on the ground. The angle subtended by the upper half of the pole at the point $$P$$ is__

The height of a tower is $$50$$ m. When angle of elevation changes from $$45^o $$ to $$ 30^o$$, the shadow of tower becomes $$x$$ metres more, find the value of $$x$$.

Find the angle of depression of a boat from the bridge at a horizontal distance of $$25$$m from the bridge, if the height of the bridge is $$25$$ m.

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $$20\ meters$$ high building are $${45}^{o}$$ and $${60}^{o}$$ respectively. Then the height of the tower is

Two poles of equal heights are standing opposite each other on either side of the road which is $$80$$ m wide. From the points between them on the road, the  elevation of the top of the poles are $${60^ \circ }$$ and $${30^ \circ }$$ respectively. Find the height of the poles.

The angle of elevation of jet fighter from $$A$$ point on the ground is $$60^0$$. After a fight of $$15$$ seconds angle of elevation changes to $$30^0$$. If the jet is flying at a speed of $$720 $$ km/hr. Find the constant height at which jet is flying. (Take $$\sqrt3= 1.732$$).

The shadow of a vertical tower on a level ground increases by $$10$$ when the altitude of the sun changes from $$45^0$$ to $$30^0$$. Find the height of the tower, correct to two decimal places.

The height of the tower is $$50$$ m  when angle of elevation changes from $$45^0$$ to $$30^0$$, the shadow of tower becomes $$x$$ meters more, find the value of $$x$$.

An aeroplane is moving one kilometer high from West to East horizontally. From a point on the ground the angle of elevation of the aeroplane is $${60}^{o}$$, and after $$10$$ seconds, the angle of elevation of the aeroplane is observed as $${30}^{o}$$, then the speed of the aeroplane in $$km/hour$$ 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 $${T_1}$$, if the angle of depression of foot of $${T_2}$$ is twice the angle of elevation of the top of $${T_2}$$ , then the width (in m) of the road between the feet of the towers $${T_1}$$ and $${T_1}$$ is: