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Example Solving Word Problems > algebra applications > geometry > triangles

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

What You Enter

Find the area of a triangle with a base of 10 inches and height of 7 inches.

What You Get
Given: B = Base = 10 INCHES
Given: H = Height = 7 INCHES
Find A = Area
A = 1/2 BH
A = 1/2(10 * 7)
 
A = 35 INCHES2

	
Solution: Y = 75/7

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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.
scalene triangles - image
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: right triangle image
    • The Pythagorean Formula applies:
      Pythagorean formula image
    • 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.
    equilateral triangle image
  • Isosceles — is a triangle that has two equal angles and two equal sides.
isosceles triangle image
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