Law of Sines and Triangle Measures

The video tutorial explains how to solve a real-world problem using the Law of Sines. A surveyor needs to find the distance across a river by choosing points A and B on one side and a reference point C on the opposite side. Given the lengths and angles, the tutorial demonstrates setting up a proportion using the Law of Sines, calculating the unknown angle, and solving for the unknown side length. The final calculation reveals the distance across the river to be approximately 127.4 meters.

What is the main objective of the problem discussed in the video?

• To determine the width of a road

• To measure the depth of a lake

• To calculate the distance across a river

• To find the height of a building

Which points are chosen by the surveyor on one side of the river?

• Points B and C

• Points A and B

• Points A and C

• Points C and D

What is the measure of angle A in the triangle?

• 47 degrees

• 90 degrees

• 82 degrees

• 51 degrees

How do we find the measure of angle C?

• By using the Pythagorean theorem

• By subtracting the measures of angles A and B from 180 degrees

• By measuring directly with a protractor

• By using the cosine rule

What is the measure of angle C?

• 60 degrees

• 82 degrees

• 47 degrees

• 51 degrees

What is the proportion set up using the Law of Sines?

• Sine of 51 degrees divided by 100 meters equals sine of 82 degrees divided by X

• Sine of 82 degrees divided by 100 meters equals sine of 51 degrees divided by X

• Sine of 51 degrees divided by X equals sine of 82 degrees divided by 100 meters

• Sine of 47 degrees divided by 100 meters equals sine of 51 degrees divided by X

What operation is performed after setting up the proportion to solve for X?

• Subtraction

• Division

• Cross multiplication

• Addition

What is the final step to find the value of X?

• Subtract 100 from both sides

• Add 100 to both sides

• Divide both sides by sine 51 degrees

• Multiply both sides by sine 51 degrees

What is the approximate length of side AC?

• 100 meters

• 127.4 meters

• 82 meters

• 51 meters

What does the length of side AC represent in this problem?

• The depth of a lake

• The width of a road

• The distance across the river

• The height of a building