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)
Just use this two step process:
Calculate "s" (half of
Step
the triangles perimeter)
1:
using:
Step Then calculate the Area
2:
using:
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 = ( 3 + 4 + 6 )/ 2 = 13/2
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:
(5.3km^2)*(14 deer/km^2) = 74.7 deer ≈ 75 deer
If this national park has 50 deer how close is
the population on this land to the average
national park population?
75 — 50 = 25
thus the land supports 25 deer less than the
average population.