How to Solve Trigonometry Questions in ECZ Mathematics

Mathematics (Grade 12 & GCE)  |  Updated March 2026  |  12 min read

Trigonometry is a major topic in ECZ Grade 12 and GCE Mathematics Paper 2. Whether calculating bearings in non-right-angled triangles or solving 3D pyramid problems, knowing which formula to apply guarantees full marks.

Senior Secondary Tip

Always ensure your scientific calculator is set to DEGREE (D or DEG) mode before starting your trigonometry exam paper!

1. Right-Angled Triangles: SOH CAH TOA

For triangles with a \(90^\circ\) right angle:

\[ \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}, \quad \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}, \quad \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \]

2. Non-Right-Angled Triangles: The Sine Rule

Use the Sine Rule when you have a known opposite side and angle pair:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
  • Finding a Side: Use \(\frac{a}{\sin A} = \frac{b}{\sin B}\).
  • Finding an Angle: Use \(\frac{\sin A}{a} = \frac{\sin B}{b}\).

3. Non-Right-Angled Triangles: The Cosine Rule

Use the Cosine Rule in two specific cases:

  1. Two sides and the included angle (SAS): Finding the third side \(a\):
    \[ a^2 = b^2 + c^2 - 2bc \cos A \]
  2. Three sides known (SSS): Finding an angle \(A\):
    \[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \]

4. Area of a Non-Right-Angled Triangle

To calculate area given two sides \(a\) and \(b\) and their included angle \(C\):

\[ \text{Area} = \frac{1}{2} a b \sin C \]

ECZ Past Paper Style Problem:

In triangle \(ABC\), \(AB = 7\text{ km}\), \(AC = 10\text{ km}\), and angle \(BAC = 52^\circ\).

  1. Calculate the length of side \(BC\) to 3 significant figures.
  2. Calculate the area of triangle \(ABC\).

Solution Part (i) - Using Cosine Rule (SAS):

Here \(b = 10\), \(c = 7\), and \(A = 52^\circ\):

\[ a^2 = 10^2 + 7^2 - 2(10)(7)\cos(52^\circ) \] \[ a^2 = 100 + 49 - 140(0.6157) \] \[ a^2 = 149 - 86.198 = 62.802 \] \[ a = \sqrt{62.802} \approx 7.92\text{ km} \]

Solution Part (ii) - Area of Triangle:

\[ \text{Area} = \frac{1}{2} (10) (7) \sin(52^\circ) = 35 \times 0.7880 \approx 27.6\text{ km}^2 \]
Rounding Rule Reminder

ECZ instructions state: non-exact numerical answers should be given to 3 significant figures, and angles in degrees to 1 decimal place. Never round intermediate values inside your calculation steps!

Teacher Tip

Train students to sketch 3D figures (such as rectangular pyramids) into separate 2D flat right-angled triangles to eliminate spatial confusion during Section B exam questions.

Frequently Asked Questions

Q1: When should I use the Sine Rule vs the Cosine Rule?

Use the Sine Rule when you know an opposite side-angle pair plus one other value (AAS or SSA). Use the Cosine Rule when you know two sides and the included angle between them (SAS) or when you know all three sides and need to find an angle (SSS).

Q2: What is the formula for the area of a non-right-angled triangle in ECZ Maths?

The area formula is Area = 1/2 * a * b * sin(C), where a and b are two side lengths and C is the included angle between them.

Q3: How many marks is Trigonometry worth in ECZ Mathematics Paper 2?

Trigonometry in ECZ Paper 2 Section B carries between 6 and 9 marks, typically divided into finding a missing side, calculating an angle, and computing the area of a triangle or 3D pyramid/prism.

Ace Your ECZ Mathematics Exams

Download past trigonometry questions with step-by-step solutions for Grade 12 and GCE candidates.

Download Maths Past Papers