HARD
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A statue stands on the top of a 2 m tall pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height (in m) of the statue. (Use 3=1.732)

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Important Questions on Heights and Distances

MEDIUM
If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30°, 45° and 60° respectively, then the ratio AB:BC, is
MEDIUM
A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from 30° to 45°, then the time taken (in min) by the car to reach the foot of the tower is
HARD
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°.  After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60° . Then the time taken (in minutes) by him, from B to reach the pillar, is
MEDIUM
ABC is a triangular park with AB=AC=100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at, A and B are cot-132 and cosec-122 respectively, then the height of the tower (in metres) is
MEDIUM
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is 
MEDIUM
Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15° with the ground. Then the distance (in m) between the poles, is
MEDIUM
PQR is a triangular park with PQ=PR=200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P,Q and R are respectively, 45°, 30° and 30°, then the height of the tower (in m) is:
HARD
A peacock perched on the top of a 12 m high tree spots a snake moving towards its hole at the base of a tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line, and they both move at the same speed. At what distance from the base of the tree will peacock catch the snake?
MEDIUM
A straight highway leads to the foot of a 50 m tall tower. From the top of the tower the angle of depression of the two cars on the highway are 30° and 60°. Then the distance between the two cars is
HARD

A sphere with centre O sits atop a pole as shown in the figure. An observer on the ground is at a distance 50 m from the foot of the pole. She notes that the angles of elevation from the observer to points P and Q on the sphere are 30° and 60° , respectively. Then, the radius of the sphere in meters is

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MEDIUM
The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30° , then the distance (in m) of the foot of the tower from the point A is:
HARD
If the angle of elevation of a cloud from a point P which is 25m above a lake be 30° and the angle of depression of reflection of the could in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is :
EASY

A ladder 10 m long is leaning against a vertical wall. It makes an angle of 60° with the ground. How far is the foot of the ladder from the wall?

MEDIUM
Two vertical poles of height, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:
MEDIUM

X is 5 m tall and he notices that he casts a shadow that is 3 m long. He then measures that the shadow cast by his school building is 30 m long. How tall is the building?

HARD
The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30o. If the angle of depression of the image of C in the lake from the point P is 60o, then PC (in m) is equal to
HARD
The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is :
MEDIUM
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that  AP=2AB. If BPC=β, then tanβ is equal to:
MEDIUM
Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation α at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is h and the distance of the foot of the smallest pole from O is a; then the distance between two consecutive poles, is
MEDIUM
Consider a triangular plot ABC with sides AB=7 m, BC=5 m and CA=6 m. A vertical lamp-post at the mid-point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is: