1. Civil Engineering
Math Concepts

2. Formulas
Efficiency = Load supported by structure ÷ Weight of structure X 100%
Area of a square = s2
Area of a rectangle = l × w
Area of a circle = πr2

3. Basic Trigonometric Functions
A right triangle has one right angle and two acute angles.
The hypotenuse is the side of a right triangle opposite the right angle. The other two sides are called legs.

4. Basic Trigonometric Functions
There are three basic trigonometric functions:
Sine
Cosine
Tangent

5. Basic Trigonometric Functions
sine  A = Length of Opposite Leg
Length of Hypotenuse
Adjacent Leg
Opposite Leg
hypotenuse A

6. Basic Trigonometric Functions
cosine  A = Length of Adjacent Leg
Length of Hypotenuse
Adjacent Leg
Opposite Leg
hypotenuse A

7. Basic Trigonometric Functions
tangent  A = Length of Opposite Leg
Length of Adjacent Leg
Adjacent Leg
Opposite Leg
hypotenuse A

8. Indirect Measurement
These functions – sine, cosine, and tangent – can be used to find measurements.
For example, if the measurement of Angle A is 45° and the length of the adjacent leg is 20 meters, the length of the opposite leg can be determined using the following equation:
tangent A = Length of Opposite Leg
Length of Adjacent Leg
tangent 45° = Length of Opposite Leg
20 meters

9. Indirect Measurement
The tangent of 45° can be found using a scientific calculator or a table of known tangent values. The tangent of 45° is 1.
1 = Length of Opposite Leg
20 meters
20 meters × 1 = Length of Opposite Leg
20 meters = Length of Opposite Leg

10. Analytical Geometry
Weight distribution in structures is a big concern for civil engineers.
Think about a platform constructed with load-bearing pillars in each corner. If the platform is a square or rectangle it would have four corners and therefore four pillars.
If a load of 1,000 pounds were placed on the platform, then each of the pillars would essentially be bearing 250 pounds of force.

11. Analytical Geometry
Now, consider that instead of four straight pillars the same platform was constructed with triangular shaped supports in each corner.
The 1,000 pound load would be distributed throughout the triangle’s sides.
Some of the force would be distributed horizontally, and some would be distributed vertically. This decreases the amount of force on each of the supports.