HP 48gII Graphing Calculator Bedienungsanleitung PDF herunterladen (Seite 245)

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cosine law, and sum of interior angles of a triangle, to solve for the other

three variables.

If the three sides are known, the area of the triangle can be calculated with

Heron’s formula

)()()( csbsassA −⋅−⋅−⋅= ,where s is known as the

semi-perimeter of the triangle, i.e.,

cba

Triangle solution using the Multiple Equation Solver (MES)

The Multiple Equation Solver (MES) is a feature that can be used to solve two

or more coupled equations. It must be pointed out, however, that the MES

does not solve the equations simultaneously. Rather, it takes the known

variables, and then searches in a list of equations until it finds one that can be

solved for one of the unknown variables. Then, it searches for another

equation that can be solved for the next unknowns, and so on, until all

unknowns have been solved for.

Creating a working directory

We will use the MES to solve for triangles by creating a list of equations

corresponding to the sine and cosine laws, the law of the sum of interior

angles, and Heron’s formula for the area. First, create a sub-directory within

HOME that we will call TRIANG, and move into that directory. See Chapter

2 for instructions on how to create a new sub-directory.

Entering the list of equations

Within TRIANG, enter the following list of equations either by typing them

directly on the stack or by using the equation writer. (Recall that ~‚a

produces the character α, and ~‚b produces the character β. The

character γ needs to be @ECHOed from ‚±):

‘SIN(α)/a = SIN(β)/b’

‘SIN(α)/a = SIN(γ)/c’

‘SIN(β)/b = SIN(γ)/c’

‘c^2 = a^2+b^2-2*a*b*COS(γ)’

‘b^2 = a^2+c^2-2*a*c*COS(β)’

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