HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 245

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 A = s ⋅ (s − a) ⋅ (s − b) ⋅ (s − c) ,where s is known as the semi-perimeter of the triangle, i.e., s = a + b + c . 2 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)' Page 7-11