Class 10 Maths — Chapter 9: SOME APPLICATIONS OF TRIGONOMETRY
Chapter 9: SOME APPLICATIONS OF TRIGONOMETRY is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 6 topics including Line of Sight, Angle of Elevation, and Angle of Depression, Modeling Word Problems with Right-Angled Triangles, Solving Problems with a Single Right-Angled Triangle. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Line of Sight, Angle of Elevation, and Angle of DepressionCore conceptline of sightangle of elevationangle of depressionhorizontal level
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▸Modeling Word Problems with Right-Angled TrianglesCore conceptdiagramright-angled triangleword problemmodeling
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▸Solving Problems with a Single Right-Angled TriangleCore concepttanSOHCAHTOAtowerladder
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▸Problems with Two Angles from a Single Pointflagstafftwo anglescommon basesystem of equations
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▸Problems with Two Angles from Different Pointsshadowcommon heighttwo observation pointssun's altitude
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▸Applying Angles of Depression in ProblemsCore conceptangle of depressionmulti-storeyed buildingalternate interior anglesparallel lines
Chapter Summary
Understanding the fundamental definitions of the line of sight (from observer's eye to object), angle of elevation (looking up from the horizontal), and angle of depression (looking down from the horizontal).
The ability to interpret a real-world scenario described in a word problem and represent it accurately as a geometric diagram involving one or more right-angled triangles, correctly labeling known and unknown sides and angles.
Applying the appropriate trigonometric ratios (sin, cos, tan) to find the unknown height or distance in scenarios that can be modeled by a single right-angled triangle. This includes accounting for the observer's height.
Solving complex problems involving two right-angled triangles that share a common base. This typically occurs when observing the top and bottom of an object (like a flagstaff on a building) from one point, requiring two trigonometric equations to be solved simultaneously.
Solving problems involving two right-angled triangles that share a common height. This scenario often arises when an object's top is observed from two different points on the ground (e.g., shadow length changing with the sun's altitude).
Solving problems where angles of depression are given. This requires understanding that due to parallel horizontal lines, the angle of depression from an observer is equal to the angle of elevation from the point being observed (alternate interior angles).
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Calculate tower height simply? Get Solution →
- Discover angles in nature? Get Solution →
- Show angle uses in games? Get Solution →
- What is the name for the line drawn from the eye of an observer to the point in the object being viewed? Get Solution →
- What is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level? Get Solution →
- What is the angle formed by the line of sight with the horizontal when the point is below the horizontal level? Get Solution →
- To calculate the height of a minar, which trigonometric ratio is suggested in the text that involves the opposite and adjacent sides? Get Solution →
- In Example 1, a tower stands vertically on the ground. What kind of angle is formed at the foot of the tower? Get Solution →
Did you know?
- 💡 Ancient Egyptians used basic trigonometry to measure land and build pyramids.
- 💡 Bees perform a "waggle dance" with specific angles to show where food is.
- 💡 Surveyors use lasers and trigonometry to precisely map out entire countries.
- 💡 Rainbows always appear at a 42-degree angle, a fixed optical trick.
- 💡 Sailors once used star angles to navigate vast oceans without GPS.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 6 key topics: Line of Sight, Angle of Elevation, and Angle of Depression, Modeling Word Problems with Right-Angled Triangles, Solving Problems with a Single Right-Angled Triangle, Problems with Two Angles from a Single Point, Problems with Two Angles from Different Points, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 9: SOME APPLICATIONS OF TRIGONOMETRY important for board exams?
Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 10?
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Can I use voice chat for this chapter?
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