Applications of Trigonometry in Real Life

Trigonometry is not just about triangles in a textbook. Any situation where you cannot directly measure a height, depth, distance or angle can often be solved using trigonometric ratios. By imagining a right triangle in the situation, we can find values that are impossible or inconvenient to measure directly.

One of the most common uses of trigonometry is finding the height of tall objects such as trees, buildings or towers without physically climbing them.

By measuring the horizontal distance and the angle of elevation, we use:

Ships, aircraft and even GPS systems use trigonometric ideas to calculate directions, distances and positions. By using angles between known points, navigators identify where they are and which direction to take.

Even the concept of latitude and longitude is based heavily on trigonometric relations on a sphere.

Architects and civil engineers use trigonometry to:

• decide the slope of a roof
• calculate the height of structures
• design safe and stable buildings
• ensure correct angles in bridges and beams

Any time an angle or slanted length is involved, trigonometry is in action.

Many physical quantities involve angles or oscillations, where trigonometry becomes essential:

• projectile motion (angle of launch)
• waves and oscillations (sine and cosine functions)
• inclined planes in mechanics
• electrical circuits using AC (sinusoidal currents)

Trigonometry was originally developed to study the positions of stars and planets. Astronomers use trigonometric formulas to:

• measure distances between celestial bodies
• locate the position of stars
• predict the movement of planets

The length of shadows cast by the sun helps determine the height of objects. This works because the sun's rays form a right triangle with the object and its shadow.

Many sports silently depend on trigonometry:

• calculating the angle to kick a football into a goal
• finding the best angle for a basketball shot
• determining how much to tilt a car in racing tracks
• measuring distances in golf and archery

Modern animations, video games and simulations rely heavily on trigonometric functions to:

• rotate objects
• simulate motion
• generate 3D perspective
• calculate lighting angles

Example: A drone hovers at a height of 40 m. The angle of depression to a person standing on the ground is \(25^\circ\). The horizontal distance is:

Thus, trigonometry helps measure distances without direct measurement.