What is Trigonometry? Trigonometry (from the Greek trigonon = three angles and metron = measure) is a part of elementary mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. Trigonometry is just a section of geometry.

Trigonometry and its applications: Trigonometry is used widely in the real life applications. It is extensively used in architecture, astronomy, electronics, optics, all types of engineering and visual perception. Another case in point for trigonometric application is estimating wildlife populations. In this case we use trigonometry in order to predict the maximum population of animals and living creations living in a particular area, which is done by heron’s formula. A good instance of this, which will be analyzed further, is calculating approximately number of deer in a national park.

Area of a Triangle from Sides You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that has been know for nearly 2000 years. It is called "Heron's Formula" after Hero of Alexandria (see below) Step 1: Calculate "s" (half of the triangles perimeter) using: Step 2: Then calculate the Area using: Just use this two step process:

There is a limitation to the number of deer in national park lands, because deer require food, water and protection from weather and predators. The average deer population in national park: 14 deer/km^2

Lets say if a national park is a triangular region with sides of 3 km, 4km and 6 km. Because we are not given enough information about the land for example the angles of triangle or its height, we have to use the heron’s formula. Applying heron’s formula: S = ( )/ 2 = 13/2 Area = √13/2 ( 13/2 — 3 )( 13/2 — 4 )( 13/2 — 6) ≈ 5.3 km^2 Area = √13/2 ( 13/2 — 3 )( 13/2 — 4 )( 13/2 — 6) ≈ 5.3 km^2

Average number of deer in 5.3 km^2: If this national park has 50 deer how close is the population on this land to the average national park population? thus the land supports 25 deer less than the average population. (5.3km^2)*(14 deer/km^2) = 74.7 deer ≈ 75 deer 75 — 50 = 25