Master Solving for the missing parts of a triangle using the law of cosines SAS

The video tutorial explains how to find missing parts of a triangle using the law of cosines and the law of sines. It begins with identifying the type of triangle and determining the appropriate law to use. The instructor demonstrates the calculation of side lengths using the law of cosines and then explains how to find angles using the law of sines, addressing the ambiguous case. The tutorial emphasizes the importance of understanding the order of operations and provides a detailed walkthrough of the calculations involved.

Why is it important to draw a triangle before deciding which law to use?

• To make the triangle look symmetrical

• To determine the type of triangle and the applicable law

• To ensure the triangle is equilateral

• To check if the triangle is right-angled

What is the correct formula for the Law of Cosines?

• a^2 = b^2 + c^2 - 2bc sin A

• a^2 = b^2 - c^2 + 2bc cos A

• a^2 = b^2 + c^2 + 2bc cos A

• a^2 = b^2 + c^2 - 2bc cos A

In the context of the Law of Cosines, what is the first step in solving for a missing side?

• Add all side lengths together

• Plug in the known values into the formula

• Multiply all angles by two

• Subtract the smallest side from the largest

What is the value of a^2 when using the Law of Cosines with sides 20, 30, and angle 60 degrees?

• 1200

• 600

• 1300

• 700

Why do we only consider the positive square root when solving for side lengths?

• Negative lengths are not possible in geometry

• Negative lengths are only used in advanced mathematics

• Negative lengths are used for angles

• Positive lengths are easier to calculate

What is the purpose of using the Law of Sines after applying the Law of Cosines?

• To calculate the missing angles

• To verify the triangle's area

• To determine the type of triangle

• To find the remaining side lengths

How can the ambiguous case be avoided when using the Law of Sines?

• By using only right-angled triangles

• By selecting the angle that is always acute

• By choosing the angle opposite the longest side

• By ensuring all angles are obtuse