Finding Missing Sides with the Law of Sines

Vincent introduces the Law of Sines and demonstrates its application in solving for a missing side of a triangle. The problem involves triangle ABC with given angles and one side. Vincent explains the Law of Sines as a proportion comparing angles to their opposite sides. He applies this law to find the length of side c, using known values and solving the equation through cross-multiplication. The final answer is calculated and rounded to the nearest hundredth, concluding the tutorial.

What is the Law of Sines used for?

• To find missing sides of a triangle when given two angles and one side

• To find missing angles in a triangle

• To calculate the area of a triangle

• To prove triangles are congruent

What information do we have about triangle ABC?

• Three angles

• One side and two angles

• Two sides and one angle

• Two angles and one side

What ratio is compared in the Law of Sines?

• The ratio of side lengths to their angles

• The ratio of angles to their cosine values

• The ratio of side lengths to their area

• The ratio of sine of angles to their opposite sides

How do you set up the equation using the Law of Sines?

• By adding the sides to the sines of their opposite angles

• By multiplying the sides by the sines of their opposite angles

• By dividing the sides by the sines of their opposite angles

• By equating the ratios of sides to the sines of their opposite angles

What is the next step after setting up the equation with the Law of Sines?

• Subtract the known angle from 180 degrees

• Divide both sides by the known side

• Add the known sides together

• Cross multiply and solve for the unknown side

What is the purpose of cross multiplying in the equation setup?

• To isolate the unknown side

• To find the value of the unknown angle

• To eliminate the denominator

• To simplify the equation

What is the final step in solving for the unknown side using the Law of Sines?

• Multiply both sides by the sine of the known angle

• Subtract the sine of the known angle from both sides

• Divide both sides by the sine of the known angle

• Add the sine of the known angle to both sides

Why is it important to ensure your calculator is in degree mode?

• To make the calculation easier

• Because radians are not used in geometry

• To ensure the sine values are calculated correctly

• Because the Law of Sines only works with degrees

How do you round off the final answer to the nearest hundredth?

• By looking at the first decimal place

• By looking at the third decimal place

• By looking at the fourth decimal place

• By looking at the second decimal place

What is the correct value of side c to the nearest hundredth?

• 15.14

• 15.15

• 15.17

• 15.16