a. The two triangles we can consider are triangles GBC and BEP.
b. The two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
c. The distance from B to E is 1200 feet, and the distance from P to E is 660 feet.
Part A: To identify a pair of similar triangles, we need to find two triangles that have the same shape, meaning they have the same corresponding angles and corresponding sides in the same ratio.
In this case, the two triangles we can consider are triangles GBC and BEP. Triangle GBC is formed by points G, B, and C, and triangle BEP is formed by points B, E, and P.
Part B: We know that two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. In this case, triangles GBC and BEP have the same corresponding angles because they are both right triangles with a 90-degree angle (angle P) and an acute angle (angle B).
For the corresponding sides, we can use the ratios given in the problem:
GB / BP = 400
BE / EP = 3
These ratios tell us that the corresponding sides of triangles GBC and BEP are proportional. Therefore, the triangles are similar.
Part C: To find the distance from B to E and from P to E, we can use the ratios we found in Part A:
GB / BP = 400
BE / EP = 3
Now, we can use these ratios to find the distances:
Distance from B to E: BE = GB * EP = 400 * 3 = 1200 feet
Distance from P to E: EP = BP * EB = 220 * 3 = 660 feet
So, the distance from B to E is 1200 feet, and the distance from P to E is 660 feet.