% Cosines Law
%
% Carlos R. Paiva
%
% 23 August 2021

close all
clear all

a = 25;  b = 13;  c = 15;  d = 10;

patch([0 a+c a+c a a 0],[0 0 b+d b+d b b],[0.8 0.8 1],'EdgeColor','none')
axis equal
axis off
hold on
patch([0 a a 0],[b b b+d b+d],[1 0.8 0.8],'EdgeColor','none')

plot([0 a+c],[0 0],'b','LineWidth',2)
plot([0 a+c],[b b],'b','LineWidth',2)
plot([0 a+c],[b+d b+d],'b','LineWidth',2)
plot([0 0],[0 b+d],'b','LineWidth',2)
plot([a a],[0 b+d],'b','LineWidth',2)
plot([a+c a+c],[0 b+d],'b','LineWidth',2)

%--------------------------------------------------------------------------
figure
%--------------------------------------------------------------------------

x_min = -10;  x_max = 80;
y_min = -200;  y_max = 1200;

n_max = 1000;
for n = 1:n_max
    x_aux = (x_max-x_min)*(n-1)/(n_max-1)+x_min;
    x(n) = x_aux;
    y(n) = -x_aux^2+61*x_aux+61;
end

plot(x,y,'b','LineWidth',2)
axis([x_min x_max y_min y_max])
ax = gca;
ax.FontSize = 20;
ax.Color = [1.0 1.0 0.8];
ax.FontName = 'Times New Roman';
grid on
hold on

b_x = 30.5;  Q_x = 991.25;

plot([b_x b_x],[y_min Q_x],'--r','LineWidth',1)
plot([x_min x_max],[Q_x Q_x],'--r','LineWidth',1)

plot(b_x,y_min,'ok','MarkerFaceColor','r','MarkerSize',6)
plot(b_x,Q_x,'ok','MarkerFaceColor','r','MarkerSize',6)

%--------------------------------------------------------------------------
figure
%--------------------------------------------------------------------------

a = 1;  b = 30;  c = 31;  d = 1;

patch([0 a+c a+c a a 0],[0 0 b+d b+d b b],[0.8 0.8 1],'EdgeColor','none')
axis equal
axis off
hold on
patch([0 a a 0],[b b b+d b+d],[1 0.8 0.8],'EdgeColor','none')

plot([0 a+c],[0 0],'b','LineWidth',2)
plot([0 a+c],[b b],'b','LineWidth',2)
plot([0 a+c],[b+d b+d],'b','LineWidth',2)
plot([0 0],[0 b+d],'b','LineWidth',2)
plot([a a],[0 b+d],'b','LineWidth',2)
plot([a+c a+c],[0 b+d],'b','LineWidth',2)