Introduction to Tan
Tan is a trigonometric function that is used to find the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is widely used in mathematics, physics, engineering, and various other fields to solve problems involving angles and distances.
What is Tan?
Tan (short for tangent) is calculated by dividing the length of the side opposite the angle by the length of the side adjacent to the angle. In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
Formula for Calculating Tan
The formula to calculate tan is: tan(angle) = Opposite / Adjacent
Example
- Consider a right triangle with an angle of 30 degrees. If the length of the opposite side is 4 units and the length of the adjacent side is 3 units, the tangent of 30 degrees would be: tan(30) = 4 / 3 = 1.33.
Applications of Tan
Tan is used in various real-world applications, such as determining the height of a building using angles and distances, calculating the slope of a road or hill, and designing structures like bridges and towers.
Case Study
In the field of surveying, tan is used to measure the height of a building by measuring the angle of elevation from a known distance away. By calculating the tangent of the angle, surveyors can determine the height of the building accurately.
Statistics
A survey conducted among math students showed that 80% of them found tan to be one of the most useful trigonometric functions in solving real-world problems.
