Class 10 Maths Chapter 9 Applications of Trigonometry Important Questions

One of the most common problems in chapter involves calculating the height of an object using trigonometry. Imagine a scenario where you are asked to find the height of a tree or a building, given the distance from the tree and the angle of elevation to its top.

To solve this, you would use the tangent function, which relates the angle of elevation to the height and distance of the object. This concept demonstrates the practical use of trigonometry in real life, such as in engineering and architecture.

This involves understanding the difference between the angle of elevation (the angle above the horizontal) and the angle of depression (the angle below the horizontal).

For example, you might be asked to calculate the distance of a ship from a lighthouse, given the height of the lighthouse and the angle of depression. This requires an understanding of complementary angles and the use of trigonometric ratios like sine, cosine, and tangent.

Trigonometry is extremely useful in finding distances that are otherwise difficult to measure directly, such as the width of a river.

A typical question might involve calculating the width of a river by forming a right-angled triangle with points on either side of the river and a point directly opposite. This problem demonstrates the use of trigonometric ratios and the concept of similar triangles.

Real-life application questions often involve scenarios like determining the height at which a kite is flying based on the length of the string and the angle of elevation.

This requires a practical application of trigonometric concepts and an understanding of how these principles apply in real-world situations. These types of questions also often test your ability to convert between different units of measurement.

Problems involving shadows are a fascinating application of trigonometry. For instance, you might be asked to find the length of a shadow cast by a building or to determine the height of an object given the length of its shadow and the position of the sun (angle of elevation). These problems require a practical understanding of how light and angles interact and how trigonometric ratios can be used to find unknown lengths.

Some problems may require the application of more than one trigonometric ratio. For example, you might be asked to find the height of a hill based on the angles of elevation taken at two different points a certain distance apart. This involves using multiple trigonometric ratios and possibly the sine or cosine rule. It tests a deeper understanding of trigonometry and its principles, as well as skills in algebraic manipulation.

These questions cover a range of applications of trigonometry in real-world scenarios, helping students understand the practical importance of this branch of mathematics. Remember, the key to mastering these problems lies in a solid understanding of trigonometric ratios and their practical applications.