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.In the given diagram , the angles of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line with it are complementary. Which labelled part in the diagram represents the height of the tower as √(ab) metres?
   • A.The line segment from the base of the tower to the point at distance a metres
   • B.The perpendicular line from the top of the tower to the ground
2. 2.The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.
3. 3.From a point on the ground, the angle of elevation of the top of a vertical tower is found to be such that its tangent is $\frac{3}{5}$. On walking 50 m towards the tower, the tangent of the new angle of elevation of the top of the tower is found to be $\frac{4}{5}$. Find the height of the tower.
4. 4.An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angle of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. What is the width of the river?
   • A.300(√3 - 1) m
   • B.300(√3 + 1) m
   • C.600 m
   • D.300√3 m
5. 5.At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is $\frac{5}{12}$. On walking 192 metres towards the tower; the tangent of the angle is found to be $\frac{3}{4}$. Find the height of the tower.