#### 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

Pilots, before taking off ask for the heading or a "vector"-

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

virtualskies.arc.nasa.gov/navigation/6.html

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