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Pre-Calculus

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Trigonometry

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Solving general triangles

Trigonometry Fun: Solve Word Problems with Boats, Buildings, and Angles!

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Trigonometry Fun: Solve Word Problems with Boats, Buildings, and Angles!
user profile picture

Selina

@suuhleena

·

93 Followers

Follow

A comprehensive guide to solving word problems involving angle changes in trigonometric contexts, focusing on practical applications of trigonometry in real-world scenarios involving heights, distances, and angles.

  • Learn to solve problems involving trigonometry word problems with angles of elevation and depression
  • Master techniques for calculating distances using trigonometric functions for boats and buildings
  • Understand how to apply trigonometric ratios to determine heights of structures and distances between objects
  • Practice solving complex problems involving moving objects and changing angles
  • Apply trigonometry to navigation and bearing calculations

7/19/2023

31

4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

View

Page 1: Basic Trigonometric Problem Solving

This page introduces fundamental concepts of solving trigonometric word problems using angles of elevation and depression. The content focuses on calculating building heights using trigonometric ratios.

Example: A 6'2" tall man looks up at a 37° angle to the top of a building from 689 inches away. The solution demonstrates converting measurements to consistent units and using tangent ratios to find the building's height.

Vocabulary: Angle of elevation - the angle formed between the horizontal plane and the line of sight looking upward.

Vocabulary: Angle of depression - the angle formed between the horizontal plane and the line of sight looking downward.

Highlight: The solution process involves:

  1. Converting all measurements to the same unit (feet)
  2. Using the tangent ratio to find the vertical height
  3. Adding the observer's height to the calculated height
4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

View

Page 3: Navigation and Bearing Problems

This page focuses on practical applications of trigonometry in maritime navigation, introducing concepts of bearings and course calculations.

Vocabulary: Bearing - the direction of an object or course of travel, measured in degrees clockwise from true north.

Example: A boat traveling at 30 knots changes course from 200° to 290°, requiring calculations of final position and bearing.

Highlight: The solution involves:

  • Vector addition for different course segments
  • Pythagorean theorem for distance calculations
  • Inverse tangent for bearing determination
4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

View

Page 2: Advanced Trigonometric Applications

This page explores more complex scenarios involving multiple angles and moving objects. The content covers three distinct problem types involving statues, boats, and rockets.

Example: A statue problem using both angles of elevation and depression to calculate total height.

Example: A cliff problem calculating distance between boats using angles of depression.

Example: A rocket launch problem determining distance and speed using changing angles of elevation.

Highlight: The problems demonstrate how to:

  • Calculate heights using multiple angles
  • Find distances between objects using angles of depression
  • Determine speed and distance using changing angles

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.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

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

4.9+

Average App Rating

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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

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Pre-Calculus

/

Trigonometry

/

Solving general triangles

Trigonometry Fun: Solve Word Problems with Boats, Buildings, and Angles!

user profile picture

Selina

@suuhleena

·

93 Followers

Follow

A comprehensive guide to solving word problems involving angle changes in trigonometric contexts, focusing on practical applications of trigonometry in real-world scenarios involving heights, distances, and angles.

  • Learn to solve problems involving trigonometry word problems with angles of elevation and depression
  • Master techniques for calculating distances using trigonometric functions for boats and buildings
  • Understand how to apply trigonometric ratios to determine heights of structures and distances between objects
  • Practice solving complex problems involving moving objects and changing angles
  • Apply trigonometry to navigation and bearing calculations

7/19/2023

31

 

11th

 

Pre-Calculus

2

4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

Page 1: Basic Trigonometric Problem Solving

This page introduces fundamental concepts of solving trigonometric word problems using angles of elevation and depression. The content focuses on calculating building heights using trigonometric ratios.

Example: A 6'2" tall man looks up at a 37° angle to the top of a building from 689 inches away. The solution demonstrates converting measurements to consistent units and using tangent ratios to find the building's height.

Vocabulary: Angle of elevation - the angle formed between the horizontal plane and the line of sight looking upward.

Vocabulary: Angle of depression - the angle formed between the horizontal plane and the line of sight looking downward.

Highlight: The solution process involves:

  1. Converting all measurements to the same unit (feet)
  2. Using the tangent ratio to find the vertical height
  3. Adding the observer's height to the calculated height
4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

Page 3: Navigation and Bearing Problems

This page focuses on practical applications of trigonometry in maritime navigation, introducing concepts of bearings and course calculations.

Vocabulary: Bearing - the direction of an object or course of travel, measured in degrees clockwise from true north.

Example: A boat traveling at 30 knots changes course from 200° to 290°, requiring calculations of final position and bearing.

Highlight: The solution involves:

  • Vector addition for different course segments
  • Pythagorean theorem for distance calculations
  • Inverse tangent for bearing determination
4-8 P9.328 Trig. Word Problems * Ex. A loft. 2in tall man looks up at a 37° angle to the top of a building. He is 689 inches away from the b

Page 2: Advanced Trigonometric Applications

This page explores more complex scenarios involving multiple angles and moving objects. The content covers three distinct problem types involving statues, boats, and rockets.

Example: A statue problem using both angles of elevation and depression to calculate total height.

Example: A cliff problem calculating distance between boats using angles of depression.

Example: A rocket launch problem determining distance and speed using changing angles of elevation.

Highlight: The problems demonstrate how to:

  • Calculate heights using multiple angles
  • Find distances between objects using angles of depression
  • Determine speed and distance using changing angles

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.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

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

4.9+

Average App Rating

13 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

Love this App ❤️, I use it basically all the time whenever I'm studying