Trigonometry isn’t just a theoretical concept; it has enormous practical applications in daily life as well. In Chapter 9 of CBSE Class 10 Math, “Some Applications of Trigonometry”, you will be studying ways in which trigonometric ratios are used in the world around you, particularly in calculating heights and distances. This chapter shows how trigonometric ratios and concepts in relation to angles of elevation and depression find applications in architectural, navigational, and engineering practices. The notes have been presented with an easy approach using concise explanations, formulas, and examples, all designed to make the chapter approachable for an exam-preparatory course.
These free CBSE Class 10 notes on Maths Chapter 9 - Some Applications of Trigonometry will equip you with the essential concepts and formulas to tackle those word problems with confidence!
In a right-angled triangle, the sides are defined as follows:
Below is a diagram to clarify these terms:
The primary trigonometric ratios used in this chapter include:
Using these ratios, students can solve for unknown sides or angles in problems involving heights and distances.
Problem 1: A 20-meter rope that is securely linked and stretched from the top of a vertical pole to the ground is being climbed by a circus performer. If the angle formed by the rope and ground level is 30°, find the pole's height.
Solution:
The length of the rope is 20 m, and the angle made by the rope with the ground level is 30°.
Given: AC = 20 m and angle C = 30°
To Find the height of the pole
Let AB be the vertical pole
In right angle ABC, using the sine formula
sin 30° = AB/AC
Using the value of sin 30 degrees, that is ½, we have
1/2 = AB/20
AB = 20/2
AB = 10
Therefore, the height of the pole is 10 m.
Problem2: Two ships are observed from the top of a 100 m lighthouse, which are on the same straight line but on two opposite sides of the lighthouse. The angles of depression to the ships are 30∘ and 45∘. Find the distance between the ships.
Solution:
As per the diagram, AB is the lighthouse, the ships are at points C & D, and the distances of the two ships from the base of the lighthouse are AC (d1) and AD (d2).
For ship 1 (θ1=45∘)
tan 45∘ = 100/d2 =1
d2=100m
For ship 2 (θ1=30∘)
tan 30∘ = Perpendicular/ Base
Distance between the ships:
D = d2 + d1 = 100+173.2 = 273.2m
The distance between the ships is approximately 273.2 m.
Problem 3: The angle of elevation of a cloud from a point h meters above the surface of a lake is , and the angle of depression of its reflection in the lake is . Prove that the height of the cloud above the lake is h ().
Solution: Let P be the cloud and Q be its reflection in the lake, as given in the figure.
Let A be the point where the observer is standing, and AB be h. Let AL = d
Let the height of the cloud above the lake = x.
To prove: x =
In PAL,
. ……..(1)
In QAL,
. ……..(2)
From equation (1) and (2),
Problem 4: An observer 1.5 meters tall is 20.5 meters away from a tower 22 meters high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Solution: Let the angle of elevation of the top of the tower =
According to the given figure,
Height of observer, CD = EB = 1.5m
Distance between observer and tower, DB = CE = 20.5m
AE = AB - EB = 22 - 1.5 = 20.5m
In triangle ACE,
tan = tan 45
= 45.
The student will be guided, given thorough information on the topic, and assisted in understanding and mastering it by these CBSE Notes for Class 10 Maths Chapter 9: Some Applications of Trigonometry. By learning about how the topic is used in real-world situations through clear explanations, solved examples, and helpful recommendations, students may confidently respond to queries.
(Session 2025 - 26)