Chapter 2: The Trigonometric Ratios

• $$\mathbf{\text{Side and Angle Relationships}}$$
• $$\mathbf{\text{Right Triangle Trigonometry}}$$
• $\mathbf{\text{Solving Right Triangles}}$

How would you measure the distance to an inaccessible obect, such as a ship at sea? In the 6th century BC, the Greek philosopher Thales estimated the distances to ships at sea using triangulation, a method for calculating distances by forming triangles. Using trigonometry and the measured length of just one side, the lengths of the other sides can be calculated.

Triangulation has been used to compute distances ever since. In the 16th century mapmakers began to use triangulation to position far-away places accurately. And as new methods in navigation and astronomy required greater precision, the idea of a survey using chains of triangles was developed.

In 1802, the East India Company embarked on the Great Trigonometrical Survey of India. Its goal was to measure the entire Indian subcontinent with scientific precision.