Скачать или смотреть Class 10 Maths | Chapter 9-Some Applications of Trigonometry |Exercise 9.1 Question 1

🟦 Class 10 Maths | Chapter 9 – Some Applications of Trigonometry | Exercise 9.1 Question 2 | Full Step-by-Step Solution

🎯 Topic: Heights and Distances – Tree Broken by Storm
📘 Chapter: Some Applications of Trigonometry
🧮 Exercise: 9.1 | Question: 2

In this video, we solve Exercise 9.1 Question 2 from NCERT Class 10 Maths Chapter 9.
You’ll learn how a real-life scenario of a tree breaking in a storm can be represented and solved using trigonometric ratios.

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🧠 Question Overview:

“A tree breaks due to a storm and the broken top touches the ground making an angle of 30° with it. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree before it was broken.”

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🪜 Step-by-Step Approach:

1️⃣ Draw the figure clearly showing:
 • Base = 8 m,
 • Angle = 30°,
 • Broken part = hypotenuse,
 • Remaining part = height standing.

2️⃣ Let the unbroken part = h m, and the broken part = x m.

3️⃣ In Δ formed by the ground and the broken part:
 \sin 30° = \frac{h}{x}
 \cos 30° = \frac{8}{x}

4️⃣ Divide (1) by (2) or use relations to find h and x.

5️⃣ Substitute values:
 sin 30° = 1/2, cos 30° = √3/2.

6️⃣ From cos 30° = 8/x ⇒ x = \frac{8}{\cos30°}= \frac{8}{\sqrt3/2}= \frac{16}{\sqrt3} m.

7️⃣ Now h = x × sin 30° = \frac{16}{\sqrt3}\times\frac12= \frac{8}{\sqrt3} m.

8️⃣ Total height = h + x = \frac{8}{\sqrt3}+\frac{16}{\sqrt3}= \frac{24}{\sqrt3}= 8\sqrt3 m ≈ 13.86 m.

✅ Therefore, the tree’s original height ≈ 13.86 m.

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💡 Concepts Covered:
• Representing word problems in right triangles
• Using sine & cosine ratios together
• Application of Trigonometry in daily life
• Relation between angles and distances

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🌟 Why This Question is Important:

This is a most-asked example in board exams to test:
✔️ Conversion of real-life story to geometry
✔️ Correct use of sine & cosine
✔️ Stepwise diagrammatic understanding

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📚 Covered Concepts and Chapters:
• NCERT Class 10 Maths Chapter 9
• Trigonometric Ratios (sin, cos)
• Exercise 9.1 – Application of Heights and Distances
• Angle of Elevation Concepts

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