Applying the law of sines when no triangle exists

The video tutorial explains how to use ratios and proportions to apply the law of sines. It demonstrates the process of cross multiplication to solve proportions and calculate the sine of an angle using a calculator. The tutorial also discusses the limitations of the inverse sine function and concludes that a triangle with given dimensions cannot exist due to geometric constraints.

What is the first step in applying the law of sines to a triangle?

• Calculate the area of the triangle.

• Find a ratio of an angle over its side length.

• Determine the type of triangle.

• Identify the longest side of the triangle.

Why is cross multiplication used when solving proportions?

• It is a shortcut for addition.

• It simplifies the equation.

• It is a method to solve for unknowns in a proportion.

• It is the only way to solve fractions.

What happens when you try to take the inverse sine of a value outside its domain?

• The sine function is recalculated.

• The value is automatically adjusted.

• The calculator returns a valid angle.

• The calculator shows an error.

Why is it impossible to create a triangle with a 150-degree angle and side lengths of 3 and 10?

• The triangle is not a right triangle.

• The angle is too large for the given side lengths.

• The side lengths are too short.

• The angles do not add up to 180 degrees.

What is a key geometric principle regarding angles and side lengths in triangles?

• The smaller the angle, the larger the side length.

• The larger the angle, the smaller the side length.

• Angles and side lengths are unrelated.

• The larger the angle, the larger the side length.