Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Angle Elevation & Depression Practice Quiz

Practice challenging problems to master angle concepts

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art themed trivia quiz about Up Down Angles for high school geometry students.

What is the angle of elevation?
The angle formed by the observer's line of sight above the horizontal
The angle formed below the horizontal
An angle equal to 90°
The angle between two vertical lines
The angle of elevation is defined as the angle between the horizontal line of sight and the line pointing upward to an object. This concept helps in solving problems related to heights and distances.
Which of the following best describes the angle of depression?
The angle between the observer's line of sight downward and the horizontal
The angle between two rising lines
The angle between the vertical and the observer's line of sight
The angle between two horizontal lines
An angle of depression is measured downward from a horizontal line to an object below. It serves as a key concept when analyzing viewpoints from an elevated position.
In a right triangle, which trigonometric ratio is defined as the ratio of the opposite side to the hypotenuse?
Sine
Cosine
Tangent
Cotangent
Sine is defined as the ratio of the length of the side opposite an angle to the hypotenuse. This ratio is fundamental in solving angle of elevation problems.
If a person looks upward from a point on the ground to the top of a building, what is this angle called?
Angle of Elevation
Angle of Depression
Right Angle
Complementary Angle
Looking upward from the horizontal forms an angle of elevation. This is used to determine the height of objects when the distance is known.
In diagrams involving angles of elevation and depression, which line is always drawn as horizontal?
The observer's line of sight at eye level
The line connecting the observer to the object
The slope of the object
A vertical line
A horizontal line drawn through the observer's eye level is used as a reference for measuring both angles of elevation and depression. This ensures that angle measurements are consistent and accurate.
A person standing 20 meters away from a building observes the angle of elevation to the top as 30°. What is the building's height relative to the observer's eye level?
Approximately 11.5 meters
Approximately 10 meters
Approximately 20 meters
Approximately 17.3 meters
Using the tangent ratio (tan 30° = height/20), the height is calculated as 20 × tan 30°, which is approximately 11.5 meters. This application shows how trigonometry helps compute heights.
If the angle of depression from the top of a 30-meter lighthouse to a boat is 15°, what is the horizontal distance from the lighthouse to the boat?
Approximately 112 meters
Approximately 120 meters
Approximately 60 meters
Approximately 15 meters
Using the tangent function (tan 15° = 30/distance), the distance is determined by rearranging the formula to distance = 30/tan 15°. This gives a result of approximately 112 meters.
A tree casts an 8-meter long shadow when the angle of elevation to its top is 40°. What is the height of the tree?
Approximately 6.7 meters
8 meters
9.4 meters
10 meters
Using the equation tan 40° = height/8, the height of the tree is calculated as 8 × tan 40°. This yields a height of approximately 6.7 meters.
A ladder leans against a wall making an angle of 75° with the ground. If the base of the ladder is 2 meters from the wall, what is the length of the ladder?
Approximately 7.73 meters
Approximately 2 meters
Approximately 5 meters
Approximately 4 meters
By applying the cosine function (cos 75° = 2/ladder length), the ladder's length is found by calculating 2/cos 75°. This results in a length of approximately 7.73 meters.
An observer on a 50-meter cliff sees a boat with an angle of depression of 10°. How far is the boat from the base of the cliff horizontally?
Approximately 283.5 meters
Approximately 500 meters
Approximately 176 meters
Approximately 50 meters
The tangent of the depression angle (tan 10°) relates the cliff height (50 meters) to the horizontal distance. Solving 50/tan 10° gives a distance of approximately 283.5 meters.
A hot air balloon hovers at a constant height. If the angle of elevation from a point on the ground changes from 30° to 45° as the observer moves closer, what does this indicate about the balloon?
The balloon's height remains constant
The balloon is rising
The balloon is descending
The balloon's height is decreasing
Even though the angle of elevation increases as the observer approaches the balloon, the balloon's actual height does not change. The change is due solely to the reduced horizontal distance.
Which trigonometric ratio is most directly used to calculate an object's height when the horizontal distance is known?
Tangent
Sine
Cosine
Secant
When the horizontal distance (adjacent side) and the height (opposite side) are known, the tangent ratio (opposite/adjacent) is directly applied to compute the height.
A 12-meter tall tree casts a shadow while a 2-meter tall post casts a 3-meter shadow at the same time. What is the length of the tree's shadow?
18 meters
12 meters
9 meters
6 meters
Using similar triangles, the ratio of height to shadow is constant. Setting up the proportion 12/x = 2/3 and solving for x gives a shadow length of 18 meters for the tree.
From a point on level ground, the angle of elevation to the top of a mountain is 20°. After moving 100 meters closer, the angle increases to 30°. Which principle allows you to calculate the mountain's height using these observations?
Trigonometric ratios in right triangles
Pythagorean theorem
Angle bisector theorem
Sum of interior angles of a triangle
This problem can be solved by setting up two right triangles with the angle of elevation and applying tangent ratios. Trigonometric ratios are used to relate the angles to the distances and height.
A surveyor stands 50 meters away from a building and measures an angle of elevation of 22° to its top. What is the approximate height of the building (assuming ground level is the observer's eye level)?
Approximately 20.2 meters
Approximately 22 meters
Approximately 25 meters
Approximately 50 meters
Using the tangent function (tan 22° = height/50), the building's height is calculated as 50 × tan 22°, which comes out to be roughly 20.2 meters.
A pilot observes the runway from his plane. From his current position, the angle of depression to the beginning of the runway is 5°. After flying 2 km closer, the angle of depression is 8°. What is the approximate altitude of the plane?
Approximately 463 meters
Approximately 350 meters
Approximately 500 meters
Approximately 600 meters
By setting up two equations using the tangent function (tan 5° = h/d and tan 8° = h/(d - 2)) and solving for the horizontal distance before finding the height, the plane's altitude is found to be roughly 463 meters.
An observer on a cliff measures an angle of depression of 12° to a point on a river and an angle of elevation of 28° to a helicopter above the river. If the horizontal distance from the base of the cliff to the river point is 150 meters, what is the height difference between the helicopter and the top of the cliff?
Approximately 80 meters
Approximately 50 meters
Approximately 100 meters
Approximately 120 meters
First, the cliff's height is calculated using tan 12° = height/150. Then, using tan 28° for the helicopter's angle of elevation, the difference in height is determined to be about 80 meters.
From a lookout point, the angle of elevation to the top of a mountain is 18°. After walking 300 meters closer, the angle increases to 22°. What is the expression for the mountain's height based on these angles?
300*(tan18*tan22)/(tan22 - tan18)
300*(tan22 - tan18)/(tan18*tan22)
300*(tan22 - tan18)
300/(tan22 - tan18)
By setting up the equations tan 18° = H/d and tan 22° = H/(d - 300) and eliminating the distance, the height is expressed as H = 300*(tan18*tan22)/(tan22 - tan18).
A balloon tethered to the ground is observed from two points along a straight line. The angle of elevation from one point is 25° and from a point 40 meters farther, it is 15°. What is the height of the balloon?
Approximately 25 meters
Approximately 30 meters
Approximately 20 meters
Approximately 35 meters
Let the distance from the closer point be d. Using tan 25° = height/d and tan 15° = height/(d + 40), a system of equations is formed and solved to yield a balloon height of about 25 meters.
An observer at point A sees the top of a tower with an angle of elevation of 40°. After moving 50 meters closer to the tower to point B, the angle increases to 55°. What is the height of the tower?
Approximately 102 meters
Approximately 80 meters
Approximately 120 meters
Approximately 90 meters
Using the tangent function from both positions (tan 40° = H/d and tan 55° = H/(d - 50)), you can solve for the distance and subsequently for the height H. The calculations lead to a tower height of roughly 102 meters.
0
{"name":"What is the angle of elevation?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the angle of elevation?, Which of the following best describes the angle of depression?, In a right triangle, which trigonometric ratio is defined as the ratio of the opposite side to the hypotenuse?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze the relationships between angles of elevation and depression in geometric figures.
  2. Apply trigonometric ratios to calculate unknown distances and heights.
  3. Solve problems involving up and down angles in real-world scenarios.
  4. Evaluate the accuracy of calculated measurements using geometric principles.
  5. Demonstrate the ability to interpret and create diagrams that represent angle problems effectively.

Angle Elevation & Depression Practice Cheat Sheet

  1. Understand the angle of elevation - The angle of elevation is measured between a horizontal line and your line of sight when you look up at an object. It's like tilting your head back to track a soaring eagle or the top of a skyscraper. onlinemathlearning.com
  2. Recognize the angle of depression - The angle of depression is the mirror image: it's the angle between the horizontal and your line of sight when you look down. Imagine peering over a balcony to spot a friend below - that's depression in action! onlinemathlearning.com
  3. Master trig ratios - Sine, cosine, and tangent are your three trusty sidekicks when tackling elevation and depression problems. Knowing which ratio to apply makes unknown heights and distances bow to your mathematical powers. onlinemathlearning.com
  4. Apply the tangent ratio - Remember tan θ = opposite / adjacent to find tricky heights or horizontal distances in right triangles. It's the fastest route to calculate how tall that tree or building really is! onlinemathlearning.com
  5. Use complementary angles - In two-point problems, the angle of elevation from one spot equals the angle of depression from the other. This symmetry can simplify your calculations and save you time. onlinemathlearning.com
  6. Sketch accurate diagrams - A clear, labeled drawing is half the battle. When you plot angles, distances, and heights neatly, you'll spot the solution path faster than a diagram-drawing ninja. mathbythepixel.com
  7. Account for observer height - Don't forget to include your eye level in the setup, since being taller or shorter changes the reference line. A small oversight here can throw off your entire answer! intellectualmath.com
  8. Combine with Pythagoras - Sometimes you'll need the Pythagorean theorem alongside your trig skills to find missing triangle sides. It's like calling in the big guns to wrap up your solution. onlinemathlearning.com
  9. Practice real-world problems - Tackling everyday scenarios - like measuring a flagpole or a mountain peak - reinforces your understanding and builds confidence. The more you practice, the less intimidating these questions become. onlinemath4all.com
  10. Review key definitions - A rock-solid grasp of elevation and depression terms is your foundation for success. Regular review ensures these concepts become second nature when exam time rolls around. twinkl.com
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker