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The real world uses trigonometry for measuring angles, together with distances and heights without physical access to objects. Various professional fields such as architecture, civil engineering, navigation, astronomy, together with computer graphic design, make extensive use of trigonometric methodologies. Every modern structure or astronomy operation depends on basic trigonometric equations as its foundation. The chapter enables to learn of spatial reasoning and introduces mathematical models as concepts. The revision notes present vital formulas combined with actual examples, together with essential concepts to help solve problems efficiently. The correct approach, along with clarity, turns trigonometry into a smart and organized method for addressing real-world problems in both academic settings and actual situations.
The chapter presents a study of how trigonometric principles apply in fact-based conditions. Students must practice all the topics of Trigonometry and their examples from the NCERT Exemplar Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry. Students should use NCERT class 10th maths notes to study concepts and to access additional materials in higher-level chapters through the NCERT Notes prepared according to the latest CBSE pattern.
Observers create an imaginary straight line that extends from their eyes toward the viewed object. The study of trigonometry requires this tool because it enables users to identify angles during specific observational heights.
The horizontal line represents an invisible straight path which runs parallel to the ground, starting from the viewer's eye level. A horizontal line establishes a reference for trigonometry to measure the angles of elevation and depression.
An observer who looks up toward an object will experience this phenomenon. To determine the measurement, the angle formed between the sightline and the eye-level horizontal line.
For Example, if a person looks at the top of a tree, the angle formed between their line of sight and the horizontal line is the angle of elevation.
An observer who looks down toward an object will experience this phenomenon. To determine the measurement, the angle formed between the sightline and the eye-level horizontal line.
For Example, If you are standing on a cliff and looking at a boat in the sea, the angle between your line of sight and the horizontal line at your eye level is the angle of depression.
The application of trigonometric ratios enables the solution of problems regarding the measurement of height and distance. The following key sequence directs a solution to these problems:
Case 1: When the Angle of Elevation is known:
For example, A tower is 30 meters high. The angle of elevation of the top of the tower from a point on the ground is 60°. Find the distance of the point from the base of the tower.
Solution: Given:
Using the formula:
Tan θ =
Tan 60° =
√3 =
X =
X = 10√3 m ≈ 17.32 m
Case 2: When the Angle of Depression is known:
For example, A lighthouse stands on a cliff 50 meters above sea level. A boat is spotted at sea, and the angle of depression from the top of the lighthouse to the boat is 30°. Find the distance of the boat from the base of the cliff.
Solution: Given:
Using the formula:
Tan θ =
Tan 30° =
x = 50√3 ≈ 86.6 meters
Students must download the notes below for each chapter to ace the topics.
Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.
Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.
To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.
Some key applications include:
Trigonometric ratios and the angle of elevation are used to determine a tower's height:
1. Identify the given values:
2. Use the trigonometric ratios.
tanθ =
3. Substitute values and calculate.
Angle of Elevation (θ): The angle formed between the horizontal line and the line of sight when a person is looking in an upward direction.
Angle of Depression (θ): The angle formed between the horizontal line and the line of sight when a person is looking in a downward direction.
Distances that are challenging to measure directly can be measured using trigonometry, including:
We can determine unknown distances by using the trigonometric ratios (sin, cos, and tan).
Admit Card Date:17 April,2025 - 17 May,2025
Exam Date:01 May,2025 - 08 May,2025
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