Single angle of elevation: height, distance and slant length 5 PYQs

• Find the height of a tower if the angle of elevation of its top is 45° from a point 20 m away from its base.Other exams 2026 · 07 Jan 2026
• The angle of elevation of the top of a building from a point 24 m away is 60°. What is the height of the building?SSC Selection Post 2026 · 24 Sep 2026
• A person standing on level ground looks up at the top of a vertical tower. The angle of elevation formed at the observer’s eye is 60°. If the tower…RRB NTPC 2026 · 18 Jun 2026
• The angle of elevation of the top of a building from a point 40 m away is 45°. What is the height of the building?RRB NTPC 2026 · 16 Jun 2026
• A vertical pole stands on level ground. From a point 20 metres (m) away from the base of the pole, the angle of elevation to the top is 45°. What is…RRB Group D 2026 · 03 Feb 2026

Angle of depression: one object, two objects on the same side or on opposite sides 2 PYQs

• From the top of a building 100√3 meters high, the angle of depression to a bicycle on the ground is 30°. What is the horizontal distance (in meters)…RRB NTPC 2026 · 15 Jun 2026
• From the top of a cliff 80 meters high, the angles of depression of two ships in the same direction are 30° and 60°. Find the distance between the…RRB NTPC 2026 · 14 Jun 2026

Shadows, the sun's elevation and similar triangles (line of sight, mirror) 5 PYQs

• A 6-metre tall vertical stick projects a 4-metre shadow onto the ground. Simultaneously, a tower casts a 28-metre shadow. What is the height of the…Other exams 2026 · 08 Jan 2026
• A mirror is placed on the ground facing the roof. A girl sees the top of a tower in the mirror which is at a distance of 210 m from the mirror. The…SSC Selection Post 2026 · 21 Sep 2026
• A tree 12 m high casts a shadow 12√3 m long. Find the angle of elevation of the sun.SSC Selection Post 2026 · 26 Sep 2026
• If the ratio of the height of a tower and the length of its shadow on the ground is √3 : 1, then the angle of elevation of the sun is:RRB NTPC 2026 · 19 Jun 2026
• A vertical stick 15 m long casts a shadow 5 m long on the ground. At the same time, a tower casts a shadow of 46.5 m long on the ground. The height…RRB Group D 2026 · 02 Feb 2026

Ladder against a wall: trigonometric ratios, triplets and sliding 3 PYQs

• A wooden cane is leaning against a wall, making an angle of 30° with the ground. If the cane is 15 m long, the distance of the point where it…SSC Selection Post 2026 · 21 Sep 2026
• A ladder 28 meters long leans against a wall, making an angle of 60° with the ground. Find the height at which the ladder touches the wall. (Use √3…RRB NTPC 2026 · 25 Mar 2026
• A ladder leans against a wall, making an angle of 60° with the ground. If the foot of the ladder is 15 metres from the wall, what is the length of…RRB NTPC 2026 · 08 May 2026

Two angles of elevation: moving towards the object, complementary angles, object on top 2 PYQs

• The angle of elevation of the top of a vertical cliff from a point is 30°. After moving 60 m towards the cliff, the angle becomes 60°. Find the…SSC Selection Post 2026 · 24 Sep 2026
• A balloon is observed from two points A and B on the ground, 1200 m apart. The angles of elevation of the balloon from these points are 60° and 30°…SSC Selection Post 2026 · 21 Sep 2026

Two objects: tower and building, two poles, a point between them 5 PYQs

• From the roof of a building 20 m high, the angle of elevation of the top of a tower is 45° and the angle of depression of its foot is 30°. Find the…SSC Selection Post 2026 · 26 Sep 2026
• A man standing on the deck of a ship, 25 m above water level, observes the angle of elevation of the top of a cliff as 60° and the angle of…SSC Selection Post 2026 · 18 Sep 2026
• Two towers of heights h_1 and h_2 subtend angles of 30° and 60° respectively at a point on the line joining their feet. If the distance between the…SSC Selection Post 2026 · 23 Sep 2026
• From the top of a building 20 m high, the angles of depression of the top and the bottom of a tower standing on the same horizontal ground are…RRB NTPC 2026 · 20 Jun 2026
• The angle of elevation of a cloud from a point h m above a lake is α and the angle of depression of its reflection in the lake is β. Find the height…SSC Selection Post 2026 · 25 Sep 2026