Topic 4 Angles of Elevation and Depression Flashcards
(30 cards)
What is the angle of elevation?
The angle formed between the horizontal line and the line of sight to an object above the horizontal.
What is the angle of depression?
The angle formed between the horizontal line and the line of sight to an object below the horizontal.
True or False: The angle of elevation is always measured from the ground up.
True
True or False: The angle of depression is measured from the object to the horizontal line.
False
Fill in the blank: The angle of elevation is measured from the _______.
horizontal line
Fill in the blank: The angle of depression is measured from the _______.
horizontal line
If a person looks up at a building and the angle of elevation is 30 degrees, what type of angle is this?
Angle of elevation
If a person looks down at a ship from a cliff, what type of angle is formed?
Angle of depression
What trigonometric function relates the opposite side and the adjacent side for angles of elevation?
Tangent
What is the formula for finding height using the angle of elevation?
Height = Distance × tan(angle of elevation)
Calculate the height of a tower if the distance from the observer is 50 meters and the angle of elevation is 45 degrees.
Height = 50 meters
True or False: The angle of elevation and the angle of depression are equal when measured from the same horizontal line.
True
What is the relationship between the angle of elevation and the angle of depression when viewing the same object?
They are equal.
If the angle of elevation is 60 degrees and the distance from the observer is 100 meters, what is the height?
Height = 100 × tan(60 degrees) = 173.21 meters
In a right triangle, what does the opposite side represent concerning the angle of elevation?
The height of the object being viewed.
What is the opposite side in relation to the angle of depression?
The vertical distance below the horizontal line to the object.
Fill in the blank: The _______ of a right triangle can be calculated using the tangent of the angle.
height
What happens to the angle of elevation as you move further away from the object?
It decreases.
If a person is 200 meters away from a building and sees it at an angle of elevation of 30 degrees, how do you find the height?
Use the formula Height = 200 × tan(30 degrees).
True or False: The height of an object can be found using the angle of depression.
True
What does a 90-degree angle of elevation indicate?
The observer is directly underneath the object.
What is the value of tan(45 degrees)?
1
If the angle of depression is 45 degrees and the observer is at a height of 100 meters, what is the horizontal distance to the object?
100 meters
What type of triangle is formed when using angles of elevation and depression?
Right triangle
