Answer:
2.5 feet
Step-by-step explanation:
Given two ladders resting against a wall at the same angle, and various lengths associated with the first ladder, you want to know how far from the wall is the base of the second ladder.
<h3>Similar triangles</h3>
The wall and the ground form a right angle, so the fact that the ladders make the same angles with the wall and ground means the geometry can be modeled by similar triangles. Similar triangles have proportional sides.
To find the distance of the second ladder from the wall, we can use the proportion ...
(distance from wall)/(ladder length) = x/(6.5 ft) = (5 ft)/(13 ft)
<h3>Solution</h3>
Multiplying this proportion by 6.5 ft gives ...
x = (6.5 ft)(5/13) = 2.5 ft
The base of the second ladder is 2.5 feet from the wall.
