Subjects

Trigonometry

Right Triangles

Modeling with Right Triangles

Fun Trigonometry: Find Missing Sides and Heights!

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Fun Trigonometry: Find Missing Sides and Heights!

Chelsea

@zuncho

626 Followers

Verified Study Note

This guide provides an in-depth overview of solving trigonometry problems using primary trig ratios, focusing on real-world applications of angles of elevation and depression in trigonometry. It covers key concepts, step-by-step problem-solving techniques, and practical examples for students learning trigonometry.

Key points:
• Explains angles of elevation and depression and their real-world applications
• Outlines a systematic approach to solving trigonometry problems
• Provides multiple worked examples demonstrating calculating height using angle of elevation and distance
• Includes practice problems for students to apply concepts

4/7/2023

MBF3C: Mathematics of Personal Finance
Day 3: Primary Trig Ratios - Applications
angle of elevation
angle of depression
object
ANGLES OF ELE

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Practical Applications of Trigonometry

This page demonstrates the application of trigonometric ratios to solve real-world problems, showcasing the versatility of trigonometry in real life problems.

Example Problems

Calculating the horizontal distance between a helicopter and a campfire using the angle of depression and altitude.
Determining the heading for a coast guard to intercept a distressed sailboat using trigonometric ratios.
Assessing the safety of a ladder's angle against a wall using trigonometric ratios.

Highlight: These examples illustrate real life applications of trigonometry in fields such as aviation, navigation, and construction safety.

Vocabulary: Angle of elevation, angle of depression, horizontal distance, heading

Example: In the helicopter problem, the angle of depression of 40° and altitude of 400 m are used to calculate the horizontal distance of 476.7 m to the campfire.

These problems demonstrate how trigonometry can be used to solve complex real-world situations, emphasizing the importance of trigonometry in real life problems and its applications in various industries.

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Trigonometry Practice Problems

This page provides a set of practice problems to reinforce the concepts of solving trigonometry problems using primary trig ratios and their real-world applications.

Practice Problems

Calculating the angle a ladder makes with the ground
Determining the length of a guy wire supporting a tower
Finding the distance from a boat to the base of a cliff
Calculating the height of a building using angle of elevation

Example: Problem 1 involves a 5-meter ladder resting against a wall, with its base 2 meters from the wall. Students must calculate the angle the ladder makes with the ground using the cosine ratio.

Highlight: These problems cover various scenarios, including construction, surveying, and maritime situations, demonstrating the wide range of real life applications of trigonometry.

The problems progressively increase in complexity, requiring students to apply multiple trigonometric concepts and ratios to solve them. This approach helps in developing problem-solving skills and understanding the practical uses of trigonometry.

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Advanced Trigonometry Applications

This page presents more complex trigonometry problems, further illustrating real world applications of angles of elevation and depression in trigonometry questions.

Advanced Problems

Calculating the height difference between two buildings using angle of depression
Determining the distance between two boats observed from a cliff
Solving a complex problem involving multiple buildings and angles

Example: In one problem, students must calculate the height of a taller building given the height of a shorter building (30.4 m), the distance between them (60 m), and the angle of depression (15°) from the top of the taller building to the top of the shorter one.

Highlight: These problems demonstrate applications of trigonometry in engineering and surveying, showing how trigonometric principles can be used to solve complex real-world spatial problems.

The increasing complexity of these problems challenges students to apply their knowledge of trigonometric ratios in multi-step calculations, reinforcing the importance of careful problem analysis and systematic solution approaches in solving trigonometry problems using primary trig ratios.

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Angles of Elevation and Depression in Trigonometry

This page introduces the concepts of angles of elevation and depression in trigonometry and outlines the steps for solving trigonometry problems using primary trig ratios.

Angle of Elevation and Depression

Definition: An angle of elevation is the angle formed between the horizontal line and the line of sight to an object above the observer. An angle of depression is the angle formed between the horizontal line and the line of sight to an object below the observer.

Steps for Solving Trigonometry Problems

Identify what needs to be calculated (angle or side)
Model the problem with a right triangle
Label the relevant sides associated with the angle
Write an equation using the trigonometric ratios
Substitute known values
Solve for the unknown measure and write a concluding statement

Example: A problem involving calculating the height of a silo is presented. Using an angle of elevation of 14° and a distance of 40 m from the silo, the height is calculated to be 10 m using the tangent ratio.

Highlight: The problem-solving steps emphasize the importance of drawing diagrams and correctly identifying the trigonometric ratios to use, which are crucial skills in solving right triangles trigonometry.

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Subjects

Trigonometry

Right Triangles

Modeling with Right Triangles

Fun Trigonometry: Find Missing Sides and Heights!

Chelsea

@zuncho

626 Followers

Verified Study Note

4/7/2023

Trigonometry

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Practical Applications of Trigonometry

This page demonstrates the application of trigonometric ratios to solve real-world problems, showcasing the versatility of trigonometry in real life problems.

Example Problems

Calculating the horizontal distance between a helicopter and a campfire using the angle of depression and altitude.
Determining the heading for a coast guard to intercept a distressed sailboat using trigonometric ratios.
Assessing the safety of a ladder's angle against a wall using trigonometric ratios.

Highlight: These examples illustrate real life applications of trigonometry in fields such as aviation, navigation, and construction safety.

Vocabulary: Angle of elevation, angle of depression, horizontal distance, heading

Example: In the helicopter problem, the angle of depression of 40° and altitude of 400 m are used to calculate the horizontal distance of 476.7 m to the campfire.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Trigonometry Practice Problems

This page provides a set of practice problems to reinforce the concepts of solving trigonometry problems using primary trig ratios and their real-world applications.

Practice Problems

Calculating the angle a ladder makes with the ground
Determining the length of a guy wire supporting a tower
Finding the distance from a boat to the base of a cliff
Calculating the height of a building using angle of elevation

Example: Problem 1 involves a 5-meter ladder resting against a wall, with its base 2 meters from the wall. Students must calculate the angle the ladder makes with the ground using the cosine ratio.

Highlight: These problems cover various scenarios, including construction, surveying, and maritime situations, demonstrating the wide range of real life applications of trigonometry.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Trigonometry Applications

This page presents more complex trigonometry problems, further illustrating real world applications of angles of elevation and depression in trigonometry questions.

Advanced Problems

Calculating the height difference between two buildings using angle of depression
Determining the distance between two boats observed from a cliff
Solving a complex problem involving multiple buildings and angles

Example: In one problem, students must calculate the height of a taller building given the height of a shorter building (30.4 m), the distance between them (60 m), and the angle of depression (15°) from the top of the taller building to the top of the shorter one.

Highlight: These problems demonstrate applications of trigonometry in engineering and surveying, showing how trigonometric principles can be used to solve complex real-world spatial problems.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Angles of Elevation and Depression in Trigonometry

This page introduces the concepts of angles of elevation and depression in trigonometry and outlines the steps for solving trigonometry problems using primary trig ratios.

Angle of Elevation and Depression

Definition: An angle of elevation is the angle formed between the horizontal line and the line of sight to an object above the observer. An angle of depression is the angle formed between the horizontal line and the line of sight to an object below the observer.

Steps for Solving Trigonometry Problems

Identify what needs to be calculated (angle or side)
Model the problem with a right triangle
Label the relevant sides associated with the angle
Write an equation using the trigonometric ratios
Substitute known values
Solve for the unknown measure and write a concluding statement

Example: A problem involving calculating the height of a silo is presented. Using an angle of elevation of 14° and a distance of 40 m from the silo, the height is calculated to be 10 m using the tangent ratio.

Highlight: The problem-solving steps emphasize the importance of drawing diagrams and correctly identifying the trigonometric ratios to use, which are crucial skills in solving right triangles trigonometry.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User