Series RTEQ.P. Code 92/0/1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Unit test · Ch 9: Some Applications of Trigonometry
Time allowed : 40 MinutesMaximum Marks : 20
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 11 questions. All questions are compulsory.
(ii)This question paper is divided into three sections – A, B and C.
(iii)In Section A, Question numbers 1 to 5 carry 1 mark each.
(iv)In Section B, Question numbers 6 to 8 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 9 to 11 are short answer (SA) type questions carrying 03 marks each.
(vi)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(vii)Use of calculators is not allowed.
SECTION A
This section comprises 5 questions of 1 mark each.
1.1
Which trigonometric ratio connects the height of an object with the horizontal distance of the observer from its foot?
2.1
A ladder 8 m long makes an angle of 30° with the ground. At what height does it touch the wall?
3.1
If the length of the shadow of a pole is equal to its height, what is the angle of elevation of the Sun?
4.1
From the top of a cliff the angle of depression of a boat is 40°. What is the angle of elevation of the top of the cliff as seen from the boat?
5.1
Define the angle of elevation.
SECTION B
This section comprises 3 very short answer (VSA) type questions of 2 marks each.
6.2
A kite is flying with a string 100 m long, which makes an angle of 60° with the ground. Assuming the string is straight, find the height of the kite. (Use √3 = 1.732)
7.2
The foot of a ladder is 5 m from a wall and the ladder makes an angle of 60° with the ground. Find the length of the ladder.
8.2
The angle of elevation of the top of a tower from a point on the ground 30 m away from its foot is 60°. Find the height of the tower. (Use √3 = 1.732)
SECTION C
This section comprises 3 short answer (SA) type questions of 3 marks each.
9.3
A boy 1.6 m tall looks at the top of a 21.6 m high building. He walks towards it so that the angle of elevation of the top changes from 30° to 60°. How far does he walk? (Use √3 = 1.732)
10.3
From the top of a 60 m high lighthouse, the angles of depression of two ships on the same side of the lighthouse, in a line with its foot, are 30° and 45°. Find the distance between the ships. (Use √3 = 1.732)
11.3
The angles of elevation of the top of a tower from two points on a line through its foot, on the same side, are 60° and 30°. The points are 24 m apart. Find the height of the tower. (Use √3 = 1.732)
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