How to use the law of sines when you have no solutions

The video tutorial discusses the application of the law of sines in solving triangles, focusing on cases where no solution exists. It explains how to determine the height of a triangle using sine and outlines conditions for no solution, such as when side length A is less than the height or when A is obtuse and less than or equal to B. An example is provided to illustrate these concepts, demonstrating calculations and the use of the law of sines.

What is a key condition for a triangle to have no solution when using the Law of Sines?

• When the angle is obtuse and the side is shorter than the height.

• When the angle is acute and the side is shorter than the height.

• When the angle is acute and the side is longer than the height.

• When the angle is obtuse and the side is longer than the height.

How do you calculate the height in a triangle when given side B and angle A?

• Multiply side B by the cotangent of angle A.

• Multiply side B by the cosine of angle A.

• Multiply side B by the tangent of angle A.

• Multiply side B by the sine of angle A.

What happens if side A is less than the height in a triangle with an acute angle?

• The triangle will have two solutions.

• The triangle will have one solution.

• The triangle will have no solution.

• The triangle will have infinite solutions.

In the context of the Law of Sines, what is the result if angle A is obtuse and side A is less than or equal to side B?

• The triangle will have two solutions.

• The triangle will have infinite solutions.

• The triangle will have one solution.

• The triangle will have no solution.

What is the significance of the value 1.66 in the practical example discussed?

• It indicates a valid solution for the triangle.

• It is the sine of angle B.

• It is outside the domain for the inverse sine function, indicating no solution.

• It is the cosine of angle A.

What is the first step in using the Law of Sines to determine if a triangle has a solution?

• Find the tangent of the given angle.

• Set up the Law of Sines equation.

• Calculate the cosine of the given angle.

• Determine the length of the hypotenuse.

Why might you encounter an error when trying to take the inverse sine of a value greater than 1?

• Because the sine function only outputs values between -1 and 1.

• Because the value is too small for the inverse sine function.

• Because the cosine function is being used incorrectly.

• Because the tangent function is being used incorrectly.