Question

Show how to calculate the distance between two inaccessible points A, B, by the use of similar triangles.

Answer 1

To calculate the distance between two inaccessible points A and B using similar triangles, you can use a method called triangulation. Triangulation involves measuring the angles to the points from two different vantage points and then using the properties of similar triangles to calculate the distance.

Step-by-step explanation:

To calculate the distance between two inaccessible points A and B using similar triangles, you can use a method called triangulation. Triangulation involves measuring the angles to the point from two different vantage points and then using the properties of similar triangles to calculate the distance. Here's how:

1. Find two vantage points from which you can measure the angles to the points A and B.
2. Measure the angles to point A from both vantage points, let's say the angles are a and b.
3. Measure the angles to point B from both vantage points, let's say the angles are c and d.
4. Using the pairs of angles (a, c) and (b, d), set up ratios using the properties of similar triangles.
5. Let x be the distance between the vantage points and AB be the distance between points A and B.
6. Set up the ratios: a/x = c/AB and b/x = d/AB.
7. Cross multiply and solve for AB: AB = (x*c)/a and AB = (x*d)/b.
8. Since AB is the same distance in both equations, equate the two equations to find AB: (x*c)/a = (x*d)/b.
9. Cancel out x and solve for AB: AB = (c*b)/(a*d).