Some Applications of Trigonometry Notes…

✓ Free notes Class 10 Math 1 study file

About these notes

Class 10 Math Some Applications of Trigonometry explains how to convert kites, towers, ladders and shadow problems into right triangles and use sin, cos, tan to find heights and distances; these notes focus on diagrams, formulas and stepwise methods. Main sub-topics: angle of elevation and depression, heights-and-distances, ladder and shadow problems, two-observer/two-angle problems, standard values for 30°, 45°, 60° and use of trig ratios. For Class 10 CBSE / Bihar Board students — ideal for revision and practising for chapter test, mock tests; search the site for important questions and MCQ.

Key points you will learn

Class 10 Math Some Applications of Trigonometry: always draw a clear right-angled diagram, mark horizontal (line of sight) and label sides
Angle of elevation/depression: measure from horizontal; angle of depression = angle of elevation to the lower point
Use tan θ = opposite/adjacent to get height from ground distance; sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse
Use exact values for 30°, 45°, 60°: sin 30° = 1/2, cos 45° = √2/2, sin 60° = √3/2, tan 60° = √3
Two-observer problems: form two right triangles, eliminate unknown distance using ratios and subtraction/addition of heights
Ladder and shadow problems: express same height or distance with different trig ratios, solve simultaneous equations
Keep units consistent (metres), show intermediate steps, round only at final answer and state units

What is inside this chapter

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Some Applications of trigonometry

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Questions students ask

What is angle of elevation and angle of depression?

Angle of elevation is the angle between the horizontal and the line of sight when you look up at an object; angle of depression is the angle between the horizontal and line of sight when you look down. Always draw the horizontal at the observer.

How to find height of a tower when distance and angle of elevation are given?

First draw a right triangle with base = given distance and angle at observer; then use tan θ = opposite/adjacent so height = distance × tan θ. Use exact values for common angles or a calculator otherwise.

Where can I find Class 10 Math Some Applications of Trigonometry notes and important questions?

The chapter notes are on Merit Spring ROH; for important questions and MCQ check the site's exam or practice sections and use chapter test and mock tests pages for additional revision practice.

When should I use exact trigonometric values rather than a calculator?

Use exact values for 30°, 45°, 60° in final answers to show radicals like √3/2 or √2/2 and avoid decimal rounding; use a calculator for other angles or intermediate checks.

How do I solve two-observer (two-angle) problems?

Draw two right triangles sharing a common vertical height or base, write tan for each angle giving two equations, then eliminate the unknown distance by subtracting or dividing the equations to solve for the required height or distance.

More Math chapters

Real Numbers Polynomials Pair of Linear Equations in Two Variables Quadratic Equations Arithmetic Progressions Triangles All chapters →

Class 10 — other subjects

Science Social Science Computer ENGLISH HINDI SANSKRIT

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