The Cosine Rule: How to Calculate Sides and Angles in Triangles

The video tutorial introduces trigonometry, focusing on the cosine rule. It explains how to use the cosine rule to calculate side lengths and angles in non-right-angled triangles. The tutorial covers the formulas for the cosine rule, demonstrates its application in solving problems, and highlights its use in navigation scenarios. Key points include labeling triangles correctly and knowing when to apply the cosine rule.

What is the primary use of trigonometry in triangles?

• To determine side lengths and angles

• To identify the type of triangle

• To find the perimeter of a triangle

• To calculate the area of a triangle

Which formula is used to find a side length using the cosine rule?

• A equals B squared plus C squared minus 2bc

• A equals B plus C minus 2bc cos A

• A squared equals B squared plus C squared

• A squared equals B squared plus C squared minus 2bc cos A

When should the cosine rule be applied?

• When only one side is known

• When the triangle is equilateral

• When all angles are known

• When two sides and the included angle are known

In the example problem, what is the value of cos x when calculated?

• -0.303

• 0.303

• -3.303

• 3.303

What is the final angle x calculated in the example problem?

• 68 degrees

• 107.7 degrees

• 90 degrees

• 45 degrees

In a navigation problem, if two boats sail at 90 km and 35 km with an angle of 68 degrees between them, what is the distance between the boats?

• 35 km

• 90 km

• 83.46 km

• 68 km

What is a key step in using the cosine rule effectively?

• Labeling the triangle accurately

• Ignoring the angles

• Using only one formula

• Assuming all sides are equal