You’re trying to find the shortest distance in meters a person would walk to go from point A to a point on side BC of the triangular field represented in the diagram. To get the shortest distance from point A to side BC, draw a perpendicular line from point A to side BC. Call the new vertex point D.
Now two smaller right triangles, ADC and ADB have been created.
From the diagram, length BC is 160 meters, AB is 100 meters, and AC is 100 meters. Each of the two right triangles formed has 100 meters as the length of its hypotenuse. What does that tell you about triangle ABC? AB and AC have the same length, so this is an isosceles triangle. That means that when you drew in the perpendicular distance from A down to D, you split the isosceles triangle ABC into two identical right triangles. Length BD is the same as length CD. So each of them is half of 160 meters, or 80 meters.
Each right triangle has an hypotenuse of 100 meters and one leg of 80 meters. This is a 3:4:5 right triangle, with each member of the ratio multiplied by 20. So AD must have length 60, and the minimum distance is 60 meters.