Plane Geometry Review : Triangle Area calculation

Area Formulas 1.  Given base and altitude Triangle: Given base and height Area = 1/2 (b)(h) 2. Given two sides and an Angle  Triangle:  Given 2 sides and angle Area = 1/2 (a) (b)sin θ 3. Given 3 sides Triangle Given 3 sides a,b,c Area = sqrt (s(s-a)(s-b)(s-c))----->...

Engineering Mathematics : Plane Geometry Part 1

Fundamental Principles Angles Acute angle = less 90 deg Obtuse angle = more than 90 and less than 180 deg Straight angle =180 deg Vertex of the angle is point where two lines meet Supplementary angles have a sum of 180 deg Complementary angles have a sum of 90 deg The base angles of an isosceles (two...

Algebra: What are the examples of Empirical formula

Some Formulas are derived by means of experimentation. Among these are the formulas discovered by pascal, Galileo and Archimedes. They are called empirical formulas. Examples of Empirical formulas: 1.1 a formula for changing temperature from Fahrenheit to centigrade. 2....

Algebra: What is the Lowest common Multiple in Algebraic Expression

The lowest common multiple ( L.C.M) of two or more arithmetical or algebraic expressions is the expression having the least number of factors which  will exactly contain each of the iven expressions.Thus the numbers 4, 6 and 12 will have 12 for their LCM for it exactly contains each of the numbers....

Algebra: How to factor a trinomial Perfect Square

From your previous topics , You learned that the square of a binomial is a trinomial perfect square. Thus , the factors of a trinomial perfect square are two binomials which may be written as the square of a binomial. To illustrate this point , let us consider the following examples. Example.1 Multiplication factoring  is...

Algebra: How to Translate verbal Statements into symbols

An equation is an important tool in problem solving but another tool which is just as necessary is representing related quantities by means of symbols. It must be recalled thatb letter like x can be used to represent the numerical value of a certain quantity. quantities related to the latter may also be expressed in terms of x . For example , if x represents the first of two consecutive...

Algebra: What is mean Proportion and How to solve it?

A proportion such as 1:2 =2:4 or a:b = b:c  is called a mean proportion because the second and the third terms are equal. In the latter b is the mean proportional between the first and the last terms a and c, respectively and c is the third proportional to a and b. Solving for the mean proportional  Given  in...

Algebra: How to solve the Equations containing decimals

Equations containing decimals are equations with fractions. hence the solution of decimal equations is similar to that of fractional equations with this difference-in decimal equation the multiplier of both members is that power of ten that will clear the equations of its decimal. Example1. Solve for x:                        ...

Algebra : How to solve a Literal equation

Equations where the known quantities are expressed as letters are called literal equations. Formulas are literal equations. Generally, the last letter of the alphabet are used to represent the unknown quantities, and the first letters, the known quantities. Examples: Solve for the unknown and check 1. 3x + 2a = 2x+5a     transposing     3x - 2x = 5a - 2a   ...