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Module 1 Summary

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Course: Math 20-2 SS
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Date: Saturday, 6 September 2025, 2:35 AM

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Table of contents

1. Module 1 Summary

Mathematics 20-2 Module 2 Summary

Module 1 Summary

 
This is a photo showing a woman using a theodolite to measure horizontal and vertical angles.

David Hiller/Photodisc/Thinkstock

 

In this module you learned how to use trigonometry to determine distances and angles indirectly in situations involving right triangles as well as situations involving oblique triangles. Indirect measurement is required in many situations, such as the following:

  • triangulation (the process used to create detailed maps over large distances)
  • determining heights (for example, of buildings or cliffs)

In particular, you learned the following mathematics:

 

Math Idea

Example

The Pythagorean theorem (a2 + b2 = c2) is only valid for right triangles.

This is a picture of a right triangle with hypotenuse of length 5 cm, a side of length 4 cm, and an unknown length f.

 

f2 + 42 = 52

 

f2 + 16 = 25

 

f2 = 9

 

f = 3 cm

The primary trigonometric ratios (SOH CAH TOA) are only valid for right triangles.

 

This is a picture of a right triangle with side lengths of 9 cm, 40 cm, and hypotenuse of length 41 cm. The angle opposite the 40 cm side has been labelled theta.

 

The sine law is valid for any triangle. It is a compact way of writing three separate equations:





The sine law can also be described in words: “The length of a side divided by the sine of the opposite angle is the same for all side-angle pairs in any triangle.”

This is a picture of an acute triangle with side lengths of 6430 m, 6000 m, and an unknown length labelled g. The angle across from the 6000 m side is 64 degrees, and the angle across from the side labelled g is 40 degrees.

 

The cosine law is valid for any triangle. There are two ways to write the cosine law, depending on whether you are solving for a missing side or a missing angle:

  • a2 = b2 + c2 − 2bc cos A

This is a picture of an acute triangle with side lengths of 3510 m, 5176 m, and 4994 m. The angle across from the 4994 m side is labelled theta.