Real life application of Trigonometry

 

Real life application of trigonometry

The concepts of trigonometry are applied in various fields to estimate distances. Let us look at some examples

Trigonometry in Astronomy

• Astronomers use trigonometry to calculate how far away from Earth stars and planets are.
• Despite the fact that we are aware of the distances between planets and stars, NASA scientists are still employing this mathematical method to construct and launch rockets and space shuttles today.
• Without knowledge of it, there would not be any satellites in orbit or missions to the moon by humans.

Trigonometry in Flight Engineers

• Trigonometry is used to calculate the speed, direction, and slope in order to determine an airplane’s path from landing to takeoff.
• Trigonometry is used to determine the ideal landing and takeoff angles and speeds, even when the wind is blowing.

For example: A pilot signals to an air traffic controller that she wants to land. She wants to know what angle of fall to take when she is currently at 40,000 feet. Her plane is 100,000 feet from the runway, as the air traffic controller can see on the radar.

We can determine the lengths of the hypotenuse and the opposite by looking at the diagram and knowing that we require θ$�$. Only this formula has both hypotenuse and opposite:

sinθ=sinθ=OppositeHypotenuse$\sin �=\sin �=\frac{��������}{����������}$

sinθ=40,0001000,000$\sin �=\frac{40,000}{1000,000}$

sinθ=0.4$\sin �=0.4$

The pilot must descend with a 23-degree angle.

Learn more about inverse trigonometric functions.

Trigonometry in Navigation

• Trigonometry is used to establish directions like the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward.
• To locate a certain location, it is used in navigation. It is also employed to calculate the separation between a location in the sea and the shore. It is employed to view the horizon as well.

Trigonometry in Measuring Heights

• Trigonometry can be used to quickly determine the height of a mountain or a tall building.
• By measuring the distance horizontally from the base and calculating the angle of elevation to the top, the height can be calculated. The perpendicular, base, and hypotenuse of a right-angled triangle will all be represented by this arrangement.

A boy is positioned next to a tree. He asks himself, “How tall is that tree?” as he looks up at it.

Using the tangent function, it can be calculated as follows: tan of angle = ratio of distance to tree height. Suppose the angle is θ$�$ after that

Suppose the distance is 30 meters and the angle is 45 degrees.

Height = 30tan45∘$\frac{30}{\tan {45}^{\circ }}$

tan45∘=1$\tan {45}^{\circ }=1$

Therefore, Height is 30 m