Height and Distance in Trigonometry

Various terminologies that help understand Height and Distance are,

  • Line of sight: It is the line drawn from the eye of an observer to the point in the object viewed by the observer.
  • The angle of Elevation: The angle between the horizontal and the line of sight joining an observation point to an elevated object is called the angle of elevation.
  • The angle of Depression: The angle between the horizontal and the line of sight joining an observation point to an object below the horizontal level is called the angle of depression.

Height and Distance | Applications of Trigonometry

Height and Distance: Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction.

Heights and Distances are the real-life applications of trigonometry which is useful to astronomers, navigators, architects, surveyors, etc. in solving problems related to heights and distances. In height and distance, we use trigonometric concepts to find the height and distance of various objects.

In this article, we have provided everything about heights and distances, their examples, and how to find heights and distances using trigonometric ratios.

Table of Content

  • Height and Distance in Trigonometry
  • How to Find Heights and Distances?
  • Trigonometric Ratios Table
  • Solved Examples on Height and Distance
  • Practice Problems on Height and Distance

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Height and Distance in Trigonometry

Various terminologies that help understand Height and Distance are,...

How to Find Heights and Distances?

Trigonometric ratios are used to measure the heights and distances of different objects. For example, in the above figure, a person is looking at the top of the tree the angle from the eye level to the top of the tree is called the angle of elevation and similarly, the angle from the top of the tree to the eyes of the person is called the angle of depression....

Trigonometric Ratios Table

The value of trigonometric ratios for different angles is very useful for solving Height and Distance problems. Thus it is advised to learn the values of trigonometric ratios for different angles. The value of various trigonometric ratios can be learned using the trigonometric table provided below,...

Solved Examples on Height and Distance

Example 1: If a pole 6 m high casts a shadow 2√3 m long on the ground, find the Sun’s elevation....

Practice Problems on Height and Distance

1. An observer standing 10 meters away from a tower measures the angle of elevation to the top of the tower as 30°. If the observer is 1.5 meters tall, find the height of the tower....

Summary – Height and Distance

Trigonometry finds extensive application in real-life scenarios, such as determining heights and distances. Key terminologies involved include the line of sight, angle of elevation, and angle of depression. The line of sight represents the path from the observer’s eye to the object being viewed. The angle of elevation refers to the angle between the horizontal and the line of sight when the object is above the observer’s eye level. Conversely, the angle of depression is the angle between the horizontal and the line of sight when the object is below the observer’s eye level. Trigonometric ratios are employed to calculate heights and distances in various situations. These ratios, along with trigonometric tables, aid in solving problems related to heights and distances, making trigonometry indispensable for astronomers, navigators, architects, and surveyors....

FAQs on Height and Distances

What is the angle of depression in trigonometry?...