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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

- Triangle Area Word Problem
- Triangle Word Problem
- Perimeter of Triangles Word Problem
- Sides of a Triangle Word Problem

###### 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 INCHES^{2}

Solution: Y = 75/7

#### General Triangle Formulas:

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

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

1 A = - Base * Height 2Perimeter 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 F

^{2}+S^{2}=H^{2}4^{2}+S^{2}=5^{2}Comment: Expand parentheses S=3 Comment: Simplify End

- The Pythagorean Formula applies:
- 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.