Sine Rule for Finding Angles

This page focuses on using the sine rule to find unknown angles in a triangle. It presents a problem where two sides and one angle of a triangle are known, and the task is to find another angle.

Example: In a triangle with sides 8.5cm and 12cm, and an angle of 42°, the sine rule is used to find another angle.

The solution process is shown step-by-step, demonstrating how to rearrange the sine rule formula to solve for an unknown angle.

Highlight: This example illustrates the versatility of the sine rule in solving for both sides and angles in non-right-angled triangles.

This page serves as an excellent resource for students looking for trigonometry sine rule explained examples, particularly useful for GCSE and higher-level studies.

Bearings in Trigonometry

This page introduces the concept of bearings and their application in trigonometry problems. It outlines the key rules for working with bearings and provides an example problem.

Definition: Bearings are used in navigation and are always calculated from North in a clockwise direction, expressed as three-digit numbers.

The page presents a complex problem involving multiple bearings and distances, demonstrating how to combine bearing calculations with trigonometric techniques.

Example: A problem involving three points P, Q, and R, with given bearings and one distance, is solved using a combination of bearing rules and the sine rule.

Highlight: This section emphasizes the practical application of trigonometry in real-world navigation scenarios.

This page is particularly useful for students studying trigonometry sine rule explained in the context of bearings and navigation problems.

Cosine Rule for Side Lengths

This page introduces the cosine rule and its application in finding side lengths of non-right-angled triangles. It explains when to use the cosine rule instead of the sine rule.

Definition: The cosine rule is expressed as a² = b² + c² - 2bc cos A, where a, b, c are sides and A is the angle opposite side a.

The page provides guidance on when to use the cosine rule, specifically when given two sides and the included angle of a triangle.

Example: A triangle with sides 7cm and 8cm and an included angle of 25° is used to demonstrate the application of the cosine rule to find the third side.

This section clearly explains when to use cosine rule, which is crucial for students learning to differentiate between various trigonometric problem-solving methods.

Cosine Rule for Finding Angles

This page focuses on using the cosine rule to find unknown angles in a triangle. It demonstrates how to rearrange the cosine rule formula to solve for an angle instead of a side length.

Definition: The rearranged cosine rule for finding an angle is cos A = (b² + c² - a²) / (2bc).

An example problem is presented to illustrate this application of the cosine rule.

Example: In a triangle with sides 5cm, 6cm, and 4cm, the cosine rule is used to find an unknown angle.

Highlight: This page emphasizes the versatility of the cosine rule in solving for both sides and angles in non-right-angled triangles.

This section provides valuable information for students seeking to understand the cosine rule formula for angle calculations in trigonometry.