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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.
A
b
B
a
C
c
α
β
ｙ
The sum of the interior angles of any triangle is always 180
o
, i.e.,
α + β + γ
=
180
o
. The sine law indicates that:
The cosine law indicates that:
a 2 = b 2 + c 2 – 2 ⋅ b ⋅ c ⋅
cos
α ,
b 2 = a 2 + c 2 – 2 ⋅ a ⋅ c ⋅
cos
β ,
c
2
= a
2
+ b
2
– 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,
.
sin sin sin
c b a
γ β α
= =