Heights and Distances

A man is standing on the horizontal plane. The angle of elevation of top of the pole is $\alpha$. If he walks a distance double the height of the pole, then the elevation of the pole is $2 \alpha$. The value of $\alpha$…

Each side of a square subtends an angle of $60^{\circ}$ at the top of a tower $h$ metre high standing in the centre of the square. If $a$ is the length of each side of the square, then

$A B C D$ is a rectangular field. A vertical lamp post of height 12 m stands at the corner $A$. If the angle of elevation of its top from $B$ is $60^{\circ}$ and from $C$ is $45^{\circ}$, then the area of the field is

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from $30^{\circ}$ to $60^{\circ}$, is

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is $100$meters, sees the balloon at an angle of elevation of $30^{\text{o}}.$ If the balloon rises…

A man is walking towards a vertical pillar in a straight path at a uniform speed. At a certain point $A$ on the path, he observes that the angle of elevation of the top of the pillar is $30^{o}.$ After walking for…

A harbour lies in the direction$60^{o}$south-west from a fort and at a distance of $30$ km from it. A ship sets out from the harbour at noon and sails due east at $10$ km/hour, then the time (in hours) in the evening at…

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

$PQR$ is a triangular park with $PQ=PR=200m$. A TV tower stands at the mid-point of $QR$. If the angles of elevation of the top of the tower from$P,Q$ and $R$ are$45^{o}$,$30^{o}$and$30^{o}$respectively, then the height…

The angular depressions of the top and the foot of a tower, as seen from the top of a second tower which is $150$ meters high and standing on the same level as the first, are $tan^{-1}\frac{4}{3}$ and…

A person standing at point $P$sees angle of elevation of the top of a building, whose base is $50$ meters away, to be $60^{o}$. Another building whose base is $20$ meters away from the base of the first building and is…

The sum of angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then, the height of the tower is