Law of Sines and Cosines

The video tutorial introduces the use of theodolites for triangulation, explaining how precise angular measurements help determine positions and directions. It covers the naming conventions for triangles, emphasizing the importance of using uppercase letters for angles and lowercase for sides. The tutorial explains the laws of sines and cosines, providing real-life applications such as calculating the height of a cliff and determining the fencing needed for a triangular field. The video highlights the practical use of trigonometry in solving real-world problems.

What is the primary function of a theodolite?

• To measure weight

• To measure speed

• To measure angular distances

• To measure temperature

According to the naming conventions of triangles, how are the sides opposite the angles labeled?

• With uppercase letters

• With numbers

• With lowercase letters

• With symbols

Which rule helps in finding a side length when two angles and another side are known?

• Pythagorean theorem

• Law of cosines

• Law of sines

• Law of tangents

In the example of Caleb's cliff jump, what is the height of the cliff?

• 112.3 feet

• 100 feet

• 150 feet

• 200 feet

What does the law of cosines help you find when two sides and the included angle are known?

• The perimeter of the triangle

• The third side

• The height of the triangle

• The area of the triangle

How much fencing is needed to enclose the farmer's triangular field?

• 1,500 meters

• 1,670 meters

• 2,000 meters

• 1,000 meters

How do lighthouse operators determine the distance of a ship from the shore?

• By measuring the ship's speed

• By using a compass

• By measuring angles and using trigonometry

• By estimating visually