Example Solving Word Problems > algebra applications > geometry > triangles

See Other Triangle Word Problem Examples solved by the Algebra Word Problem Solver: area, perimeter, hypoteneuse

What You Enter

y varies inversely proportional to x. y=3 when x=25. Find y when x= 7.

What You Get

 Y = k/X    Inverse Variation Statement
 
 3 = k / 25            //  Y = 3 WHEN X = 25 . Substitute values.
 
 k = 75          //  Constant of Proportionality
                                             
 Y = 75 / X          //  Y as a Function of  
                                             
 Y = (75 / 7 )       //  X = 7 . Substitute value.
 
 Y = (75 / 7 )       //  Y WHEN X = 7

Solution: Y = 75/7

General Triangle Formulas:

Area of Triangle = One-half the product of the Base Times the Height or

	    1                
	A = - Base * Height 
	    2

Perimeter of Triangle = Sum of the Lengths of the Sides

P = a + b + c where a, b, and c are the lengths of the sides of the triangle.

Triangle Types:

Scalene Triangles — Consist of two types
- Obtuse Triangles contain an angle with more than 90 degrees.
- Acute Triangles are triangles where all three angles are less than 90 degrees.

The Personal Algebra Tutor Solves problems of these types using:

The Law of Cosines. See example: Link to Law of Cosines Page
The Law of Sines. See example:

Right Triangle — A right triangle is a triangle with one 90 degree angle. The main features of a right triangle are the following:
- The Pythagorean Formula applies:
- Example of solutions from Personal Algebra Tutor:
  - http://www.cyberedinc.com/PAT-examples/trigonometry-Pythagorean-Theorem.html
- Example of solutions from Algebra Word Problem Solver:
  If the hypotenuse of a right triangle is 5 feet and first side is 4, find the length of the second side.
```
Let H=HYPOTENUSE
Let F=FIRST
Let S=SECOND
Given H=5
Given F=4
Given F²+S²=H²
4²+S²=5²    Comment:  Expand parentheses
S=3    Comment:  Simplify
End
```
Solutions for Trigonometry Problems using the following trig functions are available using the Personal Algebra Tutor: ? Sin(A) = a/c ? Cos(A) = b/c ? Tan(A) = a/b

Equilateral Triangles — is a triangle where all three sides are of equal length, and all three angles are 60 degrees. o The Perimeter of an Equilateral Triangles is 3 times the length of a side.

Isosceles — is a triangle that has two equal angles and two equal sides.