Determining the missing measurements of a triangle using the law of sines one case

The video tutorial explains how to solve a triangle problem using the law of sines. It begins with identifying the given acute angle and setting up relationships to find other angles. The instructor demonstrates solving for angle B using sine inverse and highlights the importance of using precise calculations to avoid rounding errors. The concept of ambiguous cases is introduced, explaining how different angles can have the same sine value. Finally, the tutorial concludes with calculating angle C and side C, ensuring all angles and sides are consistent with the triangle's properties.

What is the primary requirement to apply the Law of Sines in a triangle problem?

• Having all three angles

• Having at least one ratio of side to sine of angle

• Knowing the perimeter of the triangle

• Having two sides and one angle

Why is it important to use the second answer function on a calculator when solving for angle B?

• To check for errors in the initial input

• To automatically convert radians to degrees

• To avoid rounding errors by using the full precision of previous calculations

• To ensure the calculator is in degree mode

What is an ambiguous case in trigonometry?

• A triangle with all angles equal

• A situation where two different angles can have the same sine value

• A triangle with no right angles

• A problem with no solution

How can you determine if an ambiguous case might have two solutions?

• By ensuring the sum of angles is less than 180 degrees

• By verifying if the calculated angle is acute and checking the possibility of an obtuse angle

• By checking if the given angle is obtuse

• By measuring the sides of the triangle

Why can't the angle 140.52 degrees be used in this problem?

• It is not an acute angle

• It makes the sum of angles exceed 180 degrees

• It results in a negative side length

• It exceeds the maximum angle limit for a triangle

What is the calculated value of angle C in the problem?

• 140.52 degrees

• 65.52 degrees

• 39.48 degrees

• 75 degrees

What is the final calculated length of side C?

• 65.52

• 48.12

• 33.7

• 51.2