Year 11 - Maths
The area of any triangle
Non right-angled trigonometry
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils explore how to apply knowledge in trigonometry to non right-angled triangles.
Lesson Summary
You will learn to derive the formula for the area of any triangle.
Key Notes
- The formula for the area of a right-angled triangle is 0.5 x base x perpendicular height
- With an equilateral or isosceles triangle, you can use Pythagoras' theorem to find the height
- If you know one of the base angles, you can use the sine ratio to find the perpendicular height
- Doing this leads to the formula 0.5absinC
Vocabulary To Learn
- Area: The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
- Sine function: The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Common Mistakes To Avoid
- Using any two side lengths for the sine formula.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The formula for the area of a right-angled triangle is 0.5 x base x perpendicular height. With an equilateral or isosceles triangle, you can use Pythagoras' theorem to find the height.
2. Use this key word in a maths sentence and explain it clearly. 'Area'
The area is the size of the surface and states the number of unit squares needed to completely cover that surface. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Using any two side lengths for the sine formula. Correction: It must be two side lengths and the angle between them. So any two side lengths of the triangle can be used so long as you also use the angle between them.
More Lessons In This Unit
- Calculating the area of any triangle when the height is not known Study Guide
- Checking and securing understanding of trigonometric ratios Study Guide
- Considering the appropriate trigonometric rule Study Guide
- Drawing the sine and cosine graphs Study Guide
- Drawing the tangent graph Study Guide
- Interpreting the trigonometric graphs Study Guide
- Problem solving with non right-angled trigonometry Study Guide
- The cosine rule Study Guide
- The sine rule Study Guide
- Using the sine and cosine rules Study Guide
Browse all guides in the Year 11 Maths guide library.