This section uses Pythagorean triples and similar triangles to solve problems.
Firefighters use a ladder that is 25 meters long to reach windows of buildings above the ground floor. In this case, firefighters need to reach a window that is on the upper story of a house. They lean the ladder against the house, as shown in the diagram below. How high from the ground is the base of the window?
Step 1: Identify the right triangle in the figure by clicking on a part of the figure that represents a side of the right triangle.
Click on the blanks to reveal the answers.
Step 2: Determine the lengths of the triangle and whether or not the triangle has side lengths that are a Pythagorean triple. If so, then identify the Pythagorean triple.
Step 3: Decide if it is a Pythagorean triple. Is it a dilated version of a smaller, yet similar, right triangle? If so, state the scale factor used to generate this triangle from the smaller one.
Step 4: Relate the sides of the Pythagorean triple right triangle to the diagram of the real-life problem.
Step 5: Identify the height of the base of the window.Interactive button. Assistance may be required. _____ The height of the window is 20 meters above the ground and the longer leg of the right triangle.