RD Sharma Solutions for Class 10 Maths Chapter 12 Some Applications of Trigonometry

RD Sharma Solutions for Class 10 Maths Chapter 12 – Some Applications of Trigonometry are provided here to help students prepare effectively for their board exams. Building confidence for exams begins with thorough preparation, and having a reliable guide makes a significant difference. 

To support students in mastering Mathematics, our experts at Infinity Learn have designed comprehensive RD Sharma Solutions that serve as quick references for efficient learning. The solutions are structured in a simple, detailed manner with clear explanations, ensuring that concepts are easy to grasp.

Chapter 12, Some Applications of Trigonometry, from the RD Sharma Class 10 textbook, focuses on solving real-life problems related to heights and distances using trigonometric ratios. 

This chapter contains a single exercise based entirely on applying trigonometric concepts in practical scenarios. To understand the correct step-by-step method and approach for solving such problems, referring to the RD Sharma Solutions for Class 10 is highly recommended. All solutions are carefully crafted following the latest CBSE marking scheme, ensuring students are well-prepared for their examinations.

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1. A pole 6 m high casts a shadow 2√3 m long. Find the angle of elevation of the sun.

Solution: tan θ = 6 / (2√3) = √3. Hence, θ = 60°.

2. A ladder 10 m long reaches a window 8 m above the ground. Find the angle of elevation.

Solution: sin θ = 8 / 10 = 4/5. Therefore, θ ≈ 53.13°.

3. The angle of elevation of the top of a tower from a point is 30°. Height of tower is 50 m. Find the distance.

Solution: tan 30° = 50 / x, thus x = 50√3 ≈ 86.6 m.

4. From a point 100 m away, the angle of elevation of a building is 45°. Find the height.

Solution: tan 45° = height / 100. Thus, height = 100 m.

5. A kite string is 100 m long at an angle of 30°. Find the height of the kite.

Solution: sin 30° = height / 100. Thus, height = 50 m.

6. A man on a ship sees a lighthouse at an angle of 45°. Height of lighthouse is 30 m. Find the distance.

Solution: tan 45° = 30 / x. Thus, x = 30 m.

7. Two poles on either side of a road 100 m apart. Angles of elevation are 60° and 30°. Find distances from the point.

Solution: Using trigonometric ratios, the distances are 25 m and 75 m.

8. Shadow of a tower is √3 times the height. Find the angle of elevation.

Solution: tan θ = 1 / √3. Therefore, θ = 30°.

9. From the top of a 60 m building, the angle of depression to a car is 30°. Find the distance.

Solution: tan 30° = 60 / x. Thus, x = 60√3 ≈ 103.92 m.

10. A flagstaff stands on a 40 m tower. Angles of elevation are 60° and 45°. Find the flagstaff's height.

Solution: Height of flagstaff = 40(√3 - 1) ≈ 29.28 m.

11. A man observes a tower at 45°, moves 30 m closer, then sees it at 60°. Find the height of the tower.

Solution: After solving the equations, height ≈ 71 m.

12. Height of a pole equals its shadow length. Find the angle of elevation.

Solution: tan θ = 1. Thus, θ = 45°.

13. A man sees the top of a building at 60°, standing 40 m away. Find the building's height.

Solution: tan 60° = h / 40. Thus, h = 40√3 ≈ 69.28 m.

14. From the ground, angles of elevation of top and bottom of a water tank are 60° and 45°. Building height is 20 m. Find tank height.

Solution: Height of the tank = 20(√3 - 1) ≈ 14.64 m.

15. Top of a tree seen at 30°, after moving 100 m closer at 60°. Find the height of the tree.

Solution: After solving, the height ≈ 86.6 m.