Trigonometric Laws and Applications

This video tutorial focuses on solving word problems using the law of sines and cosines. It includes four examples: calculating distances between Coast Guard stations and a ship, determining the distance between two ships, finding the height of a tree using angles of elevation, and measuring the distance from the pitching rubber to first base on a baseball diamond. The video emphasizes understanding and applying trigonometric concepts to real-world scenarios.

What are the two main concepts discussed in the video?

• Law of Sines and Law of Tangents

• Law of Tangents and Law of Secants

• Law of Sines and Law of Cosines

• Law of Cosines and Law of Tangents

In the first example, what is the direction given for the ship's location relative to Station Abel?

• South 55 degrees West

• South 60 degrees East

• North 60 degrees West

• North 55 degrees East

How far is the ship from Station Baker in the first example?

• 135.58 miles

• 120 miles

• 150 miles

• 143.33 miles

In the second example, what is the bearing of the first ship?

• North 47 degrees East

• South 38 degrees East

• South 47 degrees West

• North 38 degrees East

How far apart are the two ships when dinner is served at 6:00 PM?

• 30 miles

• 23 miles

• 26 miles

• 36.18 miles

What is the angle of elevation from the first position to the top of the tree in the third example?

• 20 degrees

• 30 degrees

• 40 degrees

• 50 degrees

What is the height of the tree in the third example?

• 39.39 feet

• 60 feet

• 50 feet

• 40 feet

In the fourth example, what is the side length of the baseball diamond?

• 60.5 feet

• 90 feet

• 100 feet

• 120 feet

What is the distance from the pitching rubber to first base in the fourth example?

• 60.5 feet

• 90 feet

• 63.72 feet

• 70 feet

Which law is primarily used to solve the fourth example?

• Law of Cosines

• Law of Secants

• Law of Tangents

• Law of Sines