Answer
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Work Step by Step
# 9.28 (Geometry: display angles) Write a program that enables the user to drag the vertices
# of a triangle and displays the angles dynamically, as shown in Figure 9.38a.
# Change the mouse cursor to the cross-hair shape when the mouse is moved close
# to a vertex. The formula to compute angles A, B, and C (see Figure 9.38b) is given
# in Listing 3.2.
# Hint: Use the Point class to represent a point, as described in Exercise 8.17. Create
# three points at random locations initially. When the mouse is moved close to a
# point, change the cursor to a cross-hair pointer and reset the point to where the
# mouse is. Whenever a point is moved, redisplay the triangle and the angles.
from tkinter import * # Import tkinter
from random import randint
import math
width = 300
height = 200
radius = 2
class Point:
def __init__(self, x, y):
self.x = x
self.y = y
# Is point (x, y) close to this point
def isNearBy(self, x, y):
return distance(self.x, self.y, x, y) < radius + 3
def distance(x1, y1, x2, y2):
return ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)) ** 0.5
class MainGUI:
def __init__(self):
window = Tk() # Create a window
window.title("Triangle angles") # Set title
self.canvas = Canvas(window, width=width, height=height)
self.canvas.pack()
self.p1 = Point(randint(0, width - 1), randint(0, height - 1))
self.p2 = Point(randint(0, width - 1), randint(0, height - 1))
self.p3 = Point(randint(0, width - 1), randint(0, height - 1))
self.drawTriangle()
self.canvas.bind("", self.mouseMoved)
window.mainloop() # Create an event loop
def mouseMoved(self, event):
if self.closeToAPoint(event.x, event.y):
self.canvas["cursor"] = "plus"
else:
self.canvas["cursor"] = "arrow"
if self.p1.isNearBy(event.x, event.y):
self.p1.x = event.x
self.p1.y = event.y
elif self.p2.isNearBy(event.x, event.y):
self.p2.x = event.x
self.p2.y = event.y
elif self.p3.isNearBy(event.x, event.y):
self.p3.x = event.x
self.p3.y = event.y
self.drawTriangle()
def closeToAPoint(self, x, y):
return self.p1.isNearBy(x, y) or self.p2.isNearBy(x, y) or self.p3.isNearBy(x, y)
def drawTriangle(self):
self.canvas.delete("line")
self.canvas.create_line(self.p1.x, self.p1.y, self.p2.x, self.p2.y, tags="line")
self.canvas.create_line(self.p2.x, self.p2.y, self.p3.x, self.p3.y, tags="line")
self.canvas.create_line(self.p3.x, self.p3.y, self.p1.x, self.p1.y, tags="line")
a = distance(self.p2.x, self.p2.y, self.p3.x, self.p3.y)
b = distance(self.p1.x, self.p1.y, self.p3.x, self.p3.y)
c = distance(self.p1.x, self.p1.y, self.p2.x, self.p2.y)
A = math.degrees(math.acos((a * a - b * b - c * c) / (-2 * b * c)))
B = math.degrees(math.acos((b * b - a * a - c * c) / (-2 * a * c)))
C = math.degrees(math.acos((c * c - b * b - a * a) / (-2 * a * b)))
self.canvas.create_text(self.p1.x, self.p1.y, text=str(int(A)), tags="line")
self.canvas.create_text(self.p2.x, self.p2.y, text=str(int(B)), tags="line")
self.canvas.create_text(self.p3.x, self.p3.y, text=str(int(C)), tags="line")
MainGUI()
