Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?
long ladder:80ft
small ladder:50ft
Both ladders are leaning against the wall at the same angle, so the ratio of their lengths will be the same as the ratio of the opposite side (height) to the adjacent side (wall).
Let x be the length of the short ladder.
We can set up the following proportion:
50/x = 80/50
Cross multiplying, we get:
50 * 50 = 80x
2500 = 80x
Dividing both sides by 80, we get:
x = 31.25ft
Therefore, the length of the short ladder is 31.25 feet.