Some Applicatio...

From the top of a cliff, the angle of depression of car on the ground is $$60^o$$. If the car is at a distance of 30 m from the cliff. Find the height of the cliff.

 The angle of elevation of the top of an electric pole from a point $$15$$ feet away from the foot is $$30^o$$. Find the height of the pole.

The shadow of a pole standing on a horizontal plane is $$a$$ meters longer when the sun's elevation is $$\theta$$ than when it is $$\phi$$. The height of the pole will be:   {Use $$\sin(A-B) = \sin A \cos B - \sin B \cos A$$}

The angle of elevation of the top of a tower from a point on the ground, which is $$30$$ m away from the foot of the tower is $$30$$. The height of the tower is :

The shadow of a vertical tower on level ground increases by $$20$$m, when the altitude of the sun changes from angle of elevation $$60^o$$ to $$45^o$$. Find the height of the tower.

A tree, $$15$$m high, is broken by the wind in such a way that its top touches the ground and makes an angle $$30^o$$ with the ground. At what height from the bottom is the tree broken by the wind?

A person is $$x$$ m away from a tree which is $$10$$m high and angle of elevation of the top of the tree is $$30^o$$, then the value of $$x$$ is 

The angle of elevation of the top of a vertical tower from two points. $$30 \text{ m}$$ apart, and on the same straight line passing through the base of tower, are $$ 30^{\circ}  $$ and $$ 60^{\circ}  $$ respectively. The height of the tower is 

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at angle of $$60^o$$. Find the angle between the sun rays and ground at the time of the longer shadow.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height $$h$$. At a point on the plane, the angle of elevation of the bottom of the flagstaff is $$\displaystyle \alpha $$ and that of the top of the flagstaff is $$\displaystyle \beta $$ Then the
height of the tower is :