Triangle Properties and Laws of Sines

The video tutorial covers a quiz review on the Law of Sines and Law of Cosines, providing step-by-step solutions to various trigonometry problems. It includes solving for side lengths and angles in different triangle arrangements, such as AAS, SSS, SAS, and SSA. The tutorial also demonstrates real-world applications of trigonometry, like calculating distances and angles in practical scenarios.

What should you ensure about your calculator settings before starting the quiz?

• It should be in radian mode.

• It should be in scientific mode.

• It should be in graphing mode.

• It should be in degree mode.

When using the Law of Sines, what is the first step in solving for a missing side?

• Multiply both sides by the known angle.

• Divide both sides by the known side length.

• Set up a proportion using the sine of the known angle and side.

• Use the cosine of the known angle.

In an SSS triangle, which angle is typically found first using the Law of Cosines?

• The angle opposite the longest side

• The smallest angle

• The angle opposite the shortest side

• The largest angle

What is the key consideration in an SSA ambiguous case?

• The side opposite the given angle is longer than the adjacent side.

• The given angle is always acute.

• The given angle is always obtuse.

• The side opposite the given angle is shorter than the adjacent side.

How do you determine the distance between two ships using the Law of Cosines?

• By using the sine of the angle between them.

• By using the tangent of the angle between them.

• By using the secant of the angle between them.

• By using the cosine of the angle between them.

What is the first step in solving a triangle problem using the Law of Cosines?

• Identify the longest side.

• Identify the shortest side.

• Identify the opposite angle.

• Identify the included angle.

In a 30-60-90 triangle, how is the hypotenuse related to the shorter leg?

• It is twice the shorter leg.

• It is three times the shorter leg.

• It is half the shorter leg.

• It is equal to the shorter leg.

What is the relationship between the longer leg and the shorter leg in a 30-60-90 triangle?

• The longer leg is half the shorter leg.

• The longer leg is equal to the shorter leg.

• The longer leg is the shorter leg times the square root of three.

• The longer leg is twice the shorter leg.

How can you verify if a triangle with given sides and angles can exist?

• By checking if the sum of angles is 180 degrees.

• By using the Law of Sines to check for equal ratios.

• By ensuring all sides are equal.

• By using the Law of Cosines to check for equal angles.

What is the result if the sine ratios of two angles in a triangle are not equal?

• The triangle cannot exist.

• The triangle is isosceles.

• The triangle is equilateral.

• The triangle is right-angled.