# Activity3 Angles of elevation and depression

### Objectives

Understand the angle of elevation and angle of depression and what is the use of them.

### Estimated Time

40 minutes

### Prerequisites/Instructions, prior preparations, if any

know about hypotenuse, short leg, long leg,right angle and vertices of right triangle and how to measure side and angle by using ruler and Protractor.

### Materials/ Resources needed

Digital : Click here to open the file.

Non-digital : Tape measure.

### Process (How to do the activity)

Download this geogebra file from this link.

#### Procedure:

Activity : Look Up and Look Down

- When you see an object above you(Looks up),there is an angle of elevation between the horizontal and your line of sight to the object.
- When you see an object below you(Looks down),there is an angle of depression between the horizontal and your line of sight to the object
- Identify the segment that represents the line of sight.
- Identify the angle that represent the angle of elevation.
- Identify the angle that represent the angle of depression.

### Evaluation at the end of the activity

1.In the given diagram of a ladder leaning against a wall, which angle represents the ladder’s angle of elevation?

### Application level

In real world situations, we often discuss the angle of elevation and depression. The angle of elevation and depression is used often in word problems.The opposite side in this case is usually the height of the observer or height in terms of location, for example, the height of the object. The adjacent is usually the horizontal distance between the object and the observer.

Combining your skills with similar triangles, trigonometry and the Pythagorean Theorem, you are ready to tackle problems that are connected to more real world scenarios. The situations you will be examining will be specifically related to right triangles, and you will be Solving for Sides or Solving for Angles by using trigonometric functions.

For example: with angles of elevation, if two of the sides of the right triangle are known, then the formula for the angle of depression is given as below:

Tan θ =Opposite Side/Adjacent Side

or

θ = tan-1 (Opposite Side/Adjacent Side)

__ Problem__ - 1.The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower?

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