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# Trigonometry in Aviation

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by on 15 April 2015

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#### Transcript of Trigonometry in Aviation

By Jeryka and Spencer
Trigonometry in Aviation
What is used?
When taking off, they use the degree between the heading and the direction of the wind along with the airspeed, wind speed, and cosine rule. to determine the ground speed. They then calculate the positive answer from the applied quadratic equation. This is your ground speed. Once they find their ground speed they use the sine rule to calculate the degrees that is needed to be added to the heading to get across the ground.
What is Calculated?
"When approaching an airport, pilots must learn to maneuver their aircraft
visually, so that a stabilized approach to the runway can be flown at a constant approach angle.
Precise approach planning insures a smooth transition to a landing within the Touchdown Zone of the runway. Pilots must sometimes execute visual approaches that are varied in size,
shape, and angle based upon a variety of factors such as: other aircraft, obstructions, noise
abatement, or prevailing weather conditions" The same applies to taking off.
https://pumas.gsfc.nasa.gov/files/10_13_99_1.pdf
Why it matters
What is Aviation?
Aviation is the practical art of aeronautics being the design, development, production operation and use of aircraft.
dictionary.reference.com/browse/aviation?s=t
a course flown by an aircraft
. The vector includes vector quantities which represent the magnitude and direction of the aircraft.
The aircraft's speed and direction combined indicate the velocity.
Vector addition is what they call the math used to compute the product of two forces applied to an object simultaneously. Vector addition is used for wind correction problems.
The result depends on the velocity as well as the wind vector
Often times pilots correct wind problems graphically, but it can be computed more easily by trigonometry.

Example of Calculations
c^2=a^2+b^2-2ab(cosC)c
c^2=100^2+20^2-2(100)(20)(cos45)
c=87
sinB=b(sinC)/c
sinB=20(sin45)/87
B=9.4 degrees
Adding this angle to the given heading of 45 degrees gives a coure of 54.4 degrees
Law of Cosine
Law of Sine
virtualskies.arc.nasa.gov/navigtion/6.html