Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

International Baccalaureate Mathematics

Geometry and Trigonometry

Syllabus Content

Applications of right and non-right angled trigonometry, including Pythagoras’s theorem. Angles of elevation and depression. Construction of labelled diagrams from written statements

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

See all these questions

Here are some Advanced Starters on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.


Furthermore

Official Guidance, clarification and syllabus links:

Contexts may include use of bearings.

Trigonometry is a vital aspect of mathematics that deals with the relationships between the sides and angles of triangles. It is particularly useful in solving problems involving right and non-right angled triangles. Pythagoras's theorem, a fundamental principle in trigonometry, states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Angles of elevation and depression are used in trigonometry to describe the angle at which an observer looks above or below the horizontal line, respectively.

Key Formulae:
Pythagoras’s Theorem: $$ a^2 + b^2 = c^2 $$
Sine Rule: $$ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} $$
Cosine Rule: $$ c^2 = a^2 + b^2 - 2ab\cos{C} $$

Example:
Consider a right-angled triangle ABC, where angle B is a right angle, AB = 5 units and BC = 12 units. To find the length of AC (the hypotenuse), apply Pythagoras’s theorem:
$$ AC^2 = AB^2 + BC^2 \\ AC^2 = 5^2 + 12^2 \\ AC^2 = 25 + 144 \\ AC^2 = 169 \\ AC = \sqrt{169} \\ AC = 13 \text{ units} $$

This video on Pythagoras' Theorem is from Revision Village and is aimed at students taking the IB Maths Standard level course.

John Rodger,

Thursday, November 17, 2022

"Hi, I have looked for something that specifically looks at angles of elevation and depression. Unable to find these as a separate of questions. Do you have a specific of questions relating to this?
Many thanks.

[Transum: Thanks for your comment John. You can find exam-style questions on the Angles of Elevation and Depression page.]"

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.


Apple

©1997-2024 WWW.TRANSUM.ORG