Question

modeling real life a map shows the number of steps you must take to get to a treasure. however, the map is old, and the last dimension is unreadable. explain why the triangles are similar. how many steps do you take from the pyramids to the treasure?

Explanation:

Step1: Determine similarity of triangles

Since both triangles are right - angled (one angle is \(90^{\circ}\)) and they share the same non - right angle (the angle at the vertex where the line connecting the two triangles is located). By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), the two triangles are similar.

Step2: Set up proportion

Let the number of steps from the pyramids to the treasure be \(x\).
For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{240}{x}=\frac{300}{900}\)
Cross - multiply: \(300x = 240\times900\)

Step3: Solve for \(x\)

First, calculate \(240\times900=216000\)
Then, \(x=\frac{216000}{300}\)
\(x = 720\)

Answer:

The two triangles are similar by the AA (Angle - Angle) similarity criterion. The number of steps from the pyramids to the treasure is \(720\).