Are there any similar triangles in the picture? What do we know about their properties?
100 steps, see solution.
Practice makes perfect
We want to explain why the triangles on the map are similar and find the number of steps we need to take from the pyramids to the treasure. We will do these things one at a time. First, let's identify the vertices of the triangles to make our calculations easier. We will the name triangles ABC and EDC. Let's take a look at the map with the labeled vertices.
From the graph, we can see △ ABC and △ EDC are right triangles because one of their angles is a right angle. We can also see that ∠ ACB and ∠ DCE are vertical angles and we know that vertical angles are congruent. Let's mark this information on the graph.
We found that two angles in △ ABC are congruent to two angles in △ EDC. Because of this, the third angles are also congruent, so triangles are similar. Now we can use the fact that corresponding sides in similar triangles have equivalent ratios to write a ratio for our missing side length DE. Let's use x to represent the missing length in our ratio.
DE/CD=AB/BC ⇕ x/80=300/240
Finally, we can solve for x to find how many steps we need to take from the pyramids to the treasure.
