Some Applications of Trigonometry | Class 10 Mathematics Notes

Finding Heights Using Trigonometric Ratios

This section explains the method to find the height of an object such as a minar using trigonometric ratios. Given the distance from the object, the angle of elevation, and the observer's height, the height of the object can be calculated without direct measurement. The height of the minar (CD) is the sum of the height from the ground to the observer's eye level (BD = AE) and the height from the observer's eye to the top of the minar (BC). By considering the right triangle ABC, where angle A is the angle of elevation, the tangent ratio tan A = BC / AB is used to find BC, where AB is the distance from the observer to the foot of the minar. After calculating BC, adding AE gives the total height CD of the minar. This approach uses the properties of right triangles and trigonometric ratios to solve practical problems.

📊 Diagram: Fig. 9.1; Fig. 9.4

🧪 Activity: Derive height of object using given angle of elevation and distance.

🔗 Connection: Leads to solving numerical examples applying these concepts.