ICSE Class 10 Heights and Distances — Mock Test (2027)

Free online mock test for Heights and Distances (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.The shadow of a vertical tower on a level ground increases by 10 m, when the altitude of the sun changes from 45° to 30°. What is the height of the tower correct to two decimal places?
   • A.10 m
   • B.13.66 m
   • C.20 m
   • D.27.32 m
2. 2.Find the height of a building, when it is found that on walking towards it 40 m in a horizontal line through its base the angular elevation of its top changes from $30^{\circ}$ to $45^{\circ}$.
3. 3.As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse in a horizontal line with its base are 30° and 40°, respectively. The distance between the two ships, correct to the nearest metre, is:
   • A.20 m
   • B.50 m
   • C.80 m
   • D.100 m
4. 4.From the top of a light house 100 m high, the angles of depression of two ships are observed as $48^{\circ}$ and $36^{\circ}$ respectively. Find the distance between the two ships (in the nearest metre) if: (i) the ships are on the same side of the light house, (ii) the ships are on the opposite sides of the light house.
5. 5.3. A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 68° with the ground. Find the height, upto which the ladder reaches.