Height And Distances
Chapter Name : Some Applications Of Trigonometry |
Sub Topic Code : 104_10_09_02_02 |
Topic Name : Height And Distances |
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Sub Topic Name : Some Examples |
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Introduction
• Trigonometry was invented because its need arose in astronomy. Since then astronomers have used it to calculate distances from the Earth to the planets and stars. • Trigonometry is also used in geography and in navigation. The knowledge of trigonometry is used to construct maps, determine the position of an island in relation to the longitudes and latitudes.
Pre-Requisites:
• Trigonometric Functions and Ratios. • Graphical Representation of Trigonometric angles
Activity:
Use a measuring tape to find the shadow of a building. Also find its line of sight. Then, use trigonometric ratios to find out the angle of elevation.
Real Life Question:
What is the height of a tower?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Trigonometric Functions | The trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. |
| Line of Sight | The straight line between the viewer and the target. |
| Angle of Elevation | The angle of elevation of is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level. |
| Angle of Depression | The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Protractor | Use protractor to find different angles and use the angles to find out height/length of different objects. |
Real life uses :
It is used in navigation to find the distance of the shore from a point in the sea. Trigonometry is also commonly used in finding the height of towers and mountains.
Places to visit :
Use the trigonometric ratios to find out different light angles in your home.
Practical examples around us
| Examples | Explainations |
|---|---|
| Navigation in Oceans | It is used in oceanography in calculating the height of tides in oceans. |
| Distance between planets | It is used in finding the distance between celestial bodies. |
What you learn in Theory:
Different real-life applications where Trigonometric functions can be used.
What you learn in Practice:
Use trigonometric ratios to find out the angle of elevation for trees, buildings, towers etc.