Question

in MATLAB

Label not Mi published script file your results (units) and plots accordingly. Answer with complete sentences from Matlab crosoft Word. Publish all your work. Copy and paste the function files at the end of the Problem 1 The law of cosines for a triangle states that Given the lengths of sides b,, ci, and c2 and the angles As, and Az in degrees, write a script file to evaluate the length of side b2. Test your script file with b.-140 m, c2 = 120 m, c.-100 m, A1 110°, A2-130 by At C1 C2 B2 Ag

Answer 1

From the figure we have

$a^2=b_1^2+c_1^2-2b_1c_1\cos A_1$ .......Eq.1

$a^2=b_2^2+c_2^2-2b_2c_2\cos A_2$ .......Eq.2

From Eq.1 and Eq.2

$b_2^2+c_2^2-2b_2c_2\cos A_2=b_1^2+c_1^2-2b_1c_1\cos A_1$

$\Rightarrow b_2^2-2b_2c_2\cos A_2+c_2^2-b_1^2-c_1^2+2b_1c_1\cos A_1=0$

$\Rightarrow b_2^2+b_2(-2c_2\cos A_2)+(c_2^2-b_1^2-c_1^2+2b_1c_1\cos A_1)=0$

$b_2^2+k_1b_2+k_2=0$ ......Eq.3

where are constants given by $k_1=-2c_2\cos A_2\ \&\ k_2=c_2^2-b_1^2-c_1^2+2b_1c_1\cos A_1$

We need to solve the above equation (Eq.3) using MATLAB to find the solution for $b_2$

The MATLAB code to obtain the value of $b_2$ is shown below.

%cleaning the workspace
clear all
%clearing the command window
clc
%Prompting the user to enter the values of b1,c1,c2,A1 and A2
b1=input('Enter the length of b1 in meters:');
c1=input('Enter the length of c1 in meters:');
c2=input('Enter the length of c2 in meters:');
A1=input('Enter the angle A1 in degrees:');
A2=input('Enter the angle A2 in degrees:');
%calculating the constants k1 and k2
k1=-2*c2*cos(A2*pi/180);
k2=c2^2-b1^2-c1^2+2*b1*c1*cos(A1*pi/180);
%obtaining the roots of b2^2+k1*b2+k2=0
r=roots([1 k1 k2]);
%assiging the positive roots of the above equation to b2 which is the real
%solution
b2=r(r>0);
%displaying the length of b2 on the command window.
fprintf('The length of b2 is %4.4f m\n',b2)

The output on the command window for the test case inputs is

Enter the length of b1 in meters:140
Enter the length of c1 in meters:120
Enter the length of c2 in meters:100
Enter the angle A1 in degrees:110
Enter the angle A2 in degrees:130
The length of b2 is 134.7781 m