Trigonometry - Height & Distance Questions with Solutions

From the top of a viewpoint at a height of 80 m, the angles of depression of the top and bottom of a flag standing on the same plane are ${30}^{\circ }$ and ${45}^{\circ }$. Find the height of the flag.

A line segment AB of length 10 m passes through the foot of a vertical pillar, the foot lying between A and B. The top of the pillar subtends angles ${tan}^{-1}3$ and ${tan}^{-1}2$ at A and B respectively. The height of the pillar is

A man observes the angle of elevation of the top of a mountain to be ${30}^{\circ }$. He walks 1000 feet nearer and finds the angle of elevation to be ${45}^{\circ }$. What is the distance of the first point of observation from the foot of the mountain?

A person standing at a point $A$ due south of a tower observes its angle of elevation as ${60}^{\circ }$. He walks due west to a point $B$, where the angle of elevation is ${45}^{\circ }$. At a point $C$ on $AB$ produced, the angle of elevation is ${30}^{\circ }$. Then $\frac{AB}{BC}$ is equal to

The angle of elevation of the top of a tower from a point on the ground 30 m away from its foot is ${60}^{\circ }$. The height of the tower is

A tower stands vertically on level ground. From a point on the ground $30m$ away from its foot, the angle of elevation of the top of the tower is ${60}^{\circ }$. The height of the tower is

A ladder leaning against a vertical wall makes an angle of ${60}^{\circ }$ with the ground. If the foot of the ladder is $4m$ away from the wall, the length of the ladder is

The length of the shadow of a vertical pole is $\sqrt{3}$ times its height. The angle of elevation of the sun is

From the top of a lighthouse $75m$ high, the angles of depression of two ships on the same side of it, in a straight line with its foot, are ${30}^{\circ }$ and ${45}^{\circ }$. The distance between the two ships is

A kite is flying at a height of $60m$ above the ground. The string attached to it is taut and makes an angle of ${60}^{\circ }$ with the ground. The length of the string is

The angle of elevation of the top of a tower from a point on the ground is ${30}^{\circ }$. On walking $20m$ towards the tower, the angle of elevation becomes ${60}^{\circ }$. The height of the tower is

From the top of a $7m$ high building, the angle of elevation of the top of a cable tower is ${60}^{\circ }$ and the angle of depression of its foot is ${45}^{\circ }$. The height of the tower is

Angles of elevation of the top of a tower from three collinear points A, B and C on a road leading to the foot of the tower are ${30}^{\circ }$, ${45}^{\circ }$ and ${60}^{\circ }$ respectively. The ratio of AB and BC is

If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is $\alpha$, then the height of the hill is

From three collinear points A, B and C on a level ground, which are on the same side of a tower, the angles of elevation of the top of the tower are ${30}^{\circ }$, ${45}^{\circ }$ and ${60}^{\circ }$ respectively. If BC = 60 m, then AB is:

Two towers face each other separated by a distance of 25 metres. As seen from the top of the first tower, the angle of depression of the second tower's base is ${60}^{\circ }$ and that of the top is ${30}^{\circ }$. The height (in metres) of the second tower is

A tower subtends angles $\alpha$, $2\alpha$ and $3\alpha$ respectively at points A, B and C which lie on a horizontal line through the foot of the tower. Then $\frac{AB}{BC}$ is equal to

The angles of depression of the top and bottom of an 8 m tall building from the top of a multistoried building are 30° and 45°, respectively. What is the height of the multistoried building and the distance between the two buildings?

An airplane, when 4000 m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes.

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is