HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 244)

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Page 7-10

Using the Multiple Equation Solver (MES)

The multiple equation solver is an environment where you can solve a system

of multiple equations by solving for one unknown from one equation at a time.

It is not really a solver to simultaneous solutions, rather, it is a one-by-one

solver of a number of related equations. To illustrate the use of the MES for

solving multiple equations we present an application related to trigonometry in

the next section. The examples shown here are developed in the RPN mode.

Application 1 - Solution of triangles

In this section we use one important application of trigonometric functions:

calculating the dimensions of a triangle. The solution is implemented in the

calculator using the Multiple Equation Solver, or MES.

Consider the triangle ABC shown in the figure below.

ｙ

The sum of the interior angles of any triangle is always 180

, i.e., α + β + γ =

180

. The sine law indicates that:

The cosine law indicates that:

= b

+ c

– 2⋅b⋅c⋅cos α,

= a

+ c

– 2⋅a⋅c⋅cos β,

= a

+ b

– 2⋅a⋅b⋅cos γ.

In order to solve any triangle, you need to know at least three of the following

six variables: a, b, c, α, β, γ. Then, you can use the equations of the sine law,

sinsinsin

cba

βα

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HP 48gII Graphing Calculator Manual do Utilizador Página 244

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