Finding the Shortest Distance in Nature
a) What is the shortest distance between the tree and the termite mound?
In a natural setting, a chimpanzee moves east and then south to reach its lunch spot. What is the shortest distance it covers?
b) What direction does the shortest distance make, as a positive angle with respect to due east?
How can we determine the angle formed by the shortest distance and the east direction?
Answer:
a) The shortest distance between the tree and the termite mound is approximately 77.75 meters.
b) The direction of the shortest distance makes an angle of approximately 24.22 degrees or 0.42 radians with respect to due east.
When a chimpanzee navigates its way to a termite mound in nature, it takes a path that involves 70.9 meters to the east and 31.9 meters to the south. By calculating the hypotenuse of the right triangle formed by these distances using the Pythagorean Theorem, we find the shortest distance between the tree and the termite mound to be approximately 77.75 meters. This represents the direct path the chimpanzee would take if it could travel in a straight line.
To determine the direction of this shortest distance, we calculate the angle it forms with respect to due east. Using the tangent function and inverse trigonometric ratios, we find that the angle is approximately 24.22 degrees or 0.42 radians. This angle provides the direction of the shortest distance in relation to the eastward direction the chimpanzee initially took.