BASIC TRIGONOMETRY

Trignonometric Formulas sheet

THE RIGHT TRIANGLE

For a triangle to be called a right triangle, one of the interior angles must be 90 degrees. The sum of the interior angles must be 180 degrees, as with all triangles.

TRIGONOMETRIC FUNCTIONS


PYTHAGOREAN THEOREM

Given the length of the side opposite and the side adjacent of a right triangle, the hypotenuse can be calculated by the following formula:
You can actually find any third side of a triangle, if the other two sides are known.

SUM OF INTERIOR ANGLES

If "n" is the number of vertices (corners) of a closed shape, the sum of the interior angles can be found by:
What is the sum of the interior angles for the fourth shape above?
Because it has four vertices, (4-2) * 180 = 360 degrees, like any four-sided shape.

GRADE AND PERCENT GRADE

To calculate the grade, use the following formula:
For this example, the grade equals (25/500) = 0.05
The percent grade equals (25/500) * 100 = 5%

CONVERTING MAP AREA TO FIELD AREA

If you are dealing with an area, in which the unit is square feet, or some such unit, you must square the scale of the map to calculate the proper area.
Field Area = Map Area * (Map Area)^2
So if the map has a scale of 1 in. = 2000 ft., and you measure a field to have a map area of 7 square inches, the total area is:
7 * (2000)^2 = 7 * 2000 * 2000 = 28,000,000 sq. ft.
You have to multiply both the length of the field and the width of the field by the scale to get the actual distance.
This is equal to 28,000,000 sq. ft. / 43,560 sq. ft per acre = 642.8 acres.