Triangle Trigonometry

Introduction

Welcome to I Love Mathematics. This week, we will talk about Trigonometry.

In this lesson, we will focus on identifying trigonometric ratios and solve for the missing part of a right triangle using the appropriate trigonometric ratios. Making use of the very popular mnemonics SOH CAH TOA.

This is one of the basic foundations of Trigonometry. This topic lets you have a better understanding of using the idea of trigonometric ratios for solving any part of a triangle using also its other parts specifically right triangles. This is a helpful topic since this is applicable not only in your trigonometry but also in your geometry lessons. At the same time, we may not be aware, but trigonometry is used in our daily life. Some examples are given so come on and let's get started.

Task

To prepare yourself with the new topic, you must first review your prior knowledge about the parts of a triangle specifically, hypotenuse, opposite side and adjacent side followed by trigonometric ratios of a right triangle. After reviewing, you can now start to learn how to solve for the parts of a right triangle given 2 sides and an angle & a side by watching videos and links provided showing the basic solutions.

Sample exercises and real-life examples are present so that you can practice, check your answers and also check your understanding of the subject.

You can use this online scientific calculator if you don't have one because you'll be needing it to solve for the unknown.

https://www.geogebra.org/calculator?lang=en

Note: It's better to use your physical calculator in solving for practice.

Process

Process 1. Review. Check out the links for easier understanding

1. Parts of a triangle particularly Hypotenuse, opposite side, and adjacent side.

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/a/opposite-adjacent-hypotenuse

https://www.youtube.com/watch?v=zU94BB9aUgE

2. Trigonometric ratios in a right triangle

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/a/finding-trig-ratios-in-right-triangles

Process 2. Application of the trigonometric ratios in solving for the parts of a triangle.

This link shows the steps in solving for the parts of a right triangle.

https://www.mathsisfun.com/algebra/trig-finding-side-right-triangle.html

https://courses.lumenlearning.com/boundless-algebra/chapter/trigonometry-and-right-triangles/

For further understanding, watch the videos below in finding certain parts of a right triangle using trigonometric ratios.

https://www.youtube.com/watch?v=LJbqlULJcec

https://www.youtube.com/watch?v=QThmz7ZJsWM

https://www.youtube.com/watch?v=-4yuRRhwCxY

Evaluation

To check your understanding of this topic, let's have some exercises.

This link checks your familiarity with the Basic Trigonometry Ratios mainly SOH CAH TOA.

https://www.proprofs.com/quiz-school/story.php?title=basic-trigonometry-ratios

https://www.ixl.com/math/geometry/trigonometric-ratios-sin-cos-and-tan

This link checks your understanding of how to solve for the parts of a right triangle. You need a calculator for this part.

If the side is unknown,

https://www.ixl.com/math/geometry/trigonometric-ratios-find-a-side-length

If the angle is unknown,

https://www.ixl.com/math/algebra-2/trigonometric-ratios-find-an-angle-measure

Try to answer first then solutionswill be provided on the link so that you can check your own answer.

Conclusion

Trigonometry is one of the foundations of Mathematics that is relevant because it deals with the relationship between the angles and sides of triangles. It may not be too obvious but it is present in our daily life. This is just one of the basic foundations that you can use in other fields of Mathematics such as Geometry and Calculus. Mastering the basics helps you understand and learn easier higher topics in Mathematics. You will never be lost in your lessons if you're familiar with the foundations. As the saying goes, always go back to the basics.