REAL LIFE APPLICATIONS OF TRIGONOMETRY | REAL LIFE MATH.

 

Triangle trigonometry has many applications that help find unknown lengths or angle measurements. For instance, paintings, motion pictures, and televisions have ideal viewing distances in order to create the greatest possible image from the eye. The triangle is formed between the view and the top and bot- tom (or the sides) of the viewing object.

Here are the 5 best Real Life Applications of Trigonometry.

1.) In Astronomy

Astronomers use triangle trigonometry to determine distances and sizes of objects. For example, the distance from the earth to the moon, and earth to the sun, can be found by identifying their angles from the horizon during an eclipse. The height of a solar flare can also be determined by measuring the angle from the sun to the tip of the flare, and using distance information about the earth and sun.

2.) In Engineering Work

Trigonometry can be used to find unknown lengths or angle measurements. In a situation involving right triangles, only a side length and an angle measurement are needed to determine the length of an object. This information is useful to engineers, because they can find large or hard-to-measure distances without having to measure them. For example, the height of a flagpole or a tall building can be determined using a measured distance from the pole and an angle of elevation from the ground (see below).

3.) In Ship Navigation

Right-triangle trigonometry can be used to determine an unknown angle based on two lengths. For example, the navigator of a ship will try to minimize the traveling distance by adjusting the direction of the boat to account for the water’s current. If the current is moving parallel to the waterfront, then the speed of the boat observed from land will be greater due to the push from the current. Suppose that the ship is moving perpendicular to the shore at 40 feet per second and is recording a land speed of 42 feet per second.

The current will push the boat off course if it is trying to reach a destination directly across the river. Using the cosine of the angle cos θ, the ship’s navigator can determine the angle in which to rotate the boat so that it does not move off course. The cosine function is used in this case, because the two measurements known are the adjacent (the boat speed) and hypotenuse (the land speed) sides of the right triangle.

4.) In Air-Traffic controlling

Applications of right-triangle trigonometry also exist in areas outside of surveying and navigation. Air-traffic control at small airports must establish the cloud height in the evening to determine if there is enough visibility for pilots to safely land their planes. Alight source directed at a constant angle of 70° towards the clouds situated 1,000 feet from an observer, and the observer’s angle of elevation θ to the spotlight in the clouds, are sufficient information to determine the cloud height (see below).

The pilot can also use right-triangle trigonometry to determine the moment when a plane needs to descend towards the airport. If the plane descends at a large angle, the passengers may feel uneasy due to a quick drop in altitude and also may not adjust well to changes in pressure. Consequently, the pilot tries to anticipate the opportunity to descend towards the airport at a small angle, probably less than 5°. Based on the plane’s altitude, air-traffic control at the airport can determine the point at which the plane should begin to descend.

5.) In Construction Work

Construction workers can determine the length of a wheelchair ramp based on restrictions for its angle of elevation. For example, suppose an office needs to install a ramp that is inclined at most 5° from the ground. If the incline is too great, it would be difficult for handicapped people to move up the ramp on their own. Based on this information, the architect and construction workers can determine the number of turns needed in the ramp so that it will fit on the property and stay within the angle-of-elevation regulations. In addition to wheelchair ramps, a similar equation can be set up to determine the angle by which to pave a driveway so that an automobile does not scrape its bumper on the curb upon entering and leaving.

These were the 5 Best Real Life Applications of Trigonometry.