Compute the Height: The Distance Between a Point and the Opposite Side

The surface of a triangle is the product of the height times the base. In most cases, the base is the longest side, and the height is the distance between the point (vertex) that is opposite to that side and that side. By distance we mean the line that connects the point with the line, and it is vertical to the line. Thus, the height is a fundamental property of the triangle, and it is utmost important to know its value. iTopography, in iOS version 4.3.3, is equipped with a tool to compute the height.

We are going to compute the height of a regular pentagon. For that, we start the iTopography app, and we create a new project. Then we go to the Settings screen to disable the GPS device, and next we go back to the Points screen and click on the compass button to create a regular pentagon of size 1. Finally, we go to the Map screen, and we click on the pencil (top left corner).

Notice that the pencil is red. This means that no action is currently active. When we select on an action from the menu, that action will turn red, and the color of the pencil will be gray. By clicking on the pencil we see the menu with the available actions:

  • Arrange points. We drag a point, and iTopography computes its new location, e.g. new distance and angle
  • Height
  • Create subarea. We create a subarea and iTopography computes the surface of that area

We click on the Height action to activate it. In order for this action to work we need to select a point, and a line that is opposite to that point. Hence, we click on point 1, and on the line that connects points 2 and 3. This draws a line that starts from point 1, and is vertical to line that connects points 2 and 3. Also, the value of the height is printed on the screen. Note, the symbol of the right angle.

Due to the symmetry of the shape, the height from point 1 to line that connects points 4 and 5, has the same value with the calculated one. But, there is one more height that we need to compute: The height from point 1 to line that connects points 3 and 4.

If we want to compute a new height, we first need to reset the current calculation. For that, we click on the pencil button, and then we click on the height action. This will turn the pencil button back to red, and it will de-activate the height action. Next, we repeat the process that we did before, and we get the following screenshot.

Note, that those two height do not have the same value. We can repeat this process for the other points. But, do not be surprised if the height has the values that we have already computed. This is a regular pentagon, and it is s symmetric shape.