About This Chapter
Measurement & Trigonometry - Chapter Summary
This engaging chapter outlines the concepts of trigonometry and measurement. Our instructors explain how to apply scale factors to the area, volume and perimeter of similar figures, as well as how to use the Pythagorean Theorem and trigonometry to solve right triangles. In addition, you'll learn about using the law of sines to solve a triangle. Other topics include understanding compass bearings and how to specify them. After you review these lessons, you will be ready to do the following:
- Find the area of a triangle using sine
- Understand why using the law of sines sometimes results in two answers
- Use the law of cosines to solve oblique triangles
- Utilize compass bearings to solve real-life problems
Our learning tools are a fun and easy way to study for a test or finish your homework. Each video or text lesson is followed by a quiz so you can test your knowledge. Or take the quizzes and chapter test as a great test prep exercise to see how you'd score. You can use the video tabs feature if you need to go back and review specific sections of a video lesson rather than watch the entire video over again.
1. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.
2. Solving Right Triangles Using Trigonometry & the Pythagorean Theorem
The Pythagorean Theorem is one of the most well-known and useful math equations. Its simple form and abundant uses make it one of the most helpful processes to learn in math. In this lesson, learn how to solve right triangles using the Pythagorean Theorem.
3. Using Sine to Find the Area of a Triangle
Since you first started working with triangles in math class, chances are you've been exposed to the formula for the area of a triangle. However, that is only good if you know the height of the triangle. This lesson shows you how to get around that.
4. Using the Law of Sines to Solve a Triangle
After watching this video lesson, you will be able to use the law of sines to find a missing side of a triangle as well as a missing angle of a triangle. Learn what you need to know about the triangle in order to use the formula.
5. The Ambiguous Case of the Law of Sines
You might think that all math in very concrete, that an answer or a law is always right. But this is not always so. See, in certain situations, the law of sines actually give you two answers.
6. Solving Oblique Triangles Using the Law of Cosines
After watching this video lesson, you will be able to use the law of cosines to help you find a missing side or missing angle of any kind of triangle. Also, you will see what oblique triangles are.
7. Compass Bearings: Definition & Types
Before GPS, navigation was accomplished using compass bearings. In this lesson, we'll discover how to find locations using the following methods: standard compass bearings, other compass bearings, and true bearings.
8. Solving Real World Problems With Compass Bearings
There are several methods to indicate which way an object is heading by using a compass. In this lesson, we will focus on three figure compass bearings to solve real world problems.
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Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
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- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
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- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Paths & Circuits
- Problem Solving With Networks
- Geometric Solids
- Spherical Geometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
- VCE Further Mathematics Flashcards