8. Two ladders are leaning against a wall at the same angle, as shown. How long is the short
ladder? long ladder 60ft wall 40ft short ladder 10ft
bruh whats the answer
To determine the length of the short ladder, we can use the concept of similar triangles. The two ladders are leaning against the wall at the same angle, so the triangles they form with the wall are similar.
Let's denote the length of the short ladder as "x". We can set up the following proportion using the lengths:
(short ladder length) / (wall length) = (long ladder length) / (wall length)
Substituting the given values:
x / 40ft = 60ft / 40ft
Simplifying the equation:
x / 40ft = 3/2
To solve for x, we can cross-multiply:
2x = 3 * 40ft
2x = 120ft
Dividing both sides by 2:
x = 60ft
Therefore, the short ladder is 60ft long.
To determine the length of the short ladder, you can use the concept of similar triangles. Similar triangles have proportional sides, meaning that the ratio of the corresponding sides is the same.
In this scenario, you have two similar triangles: one formed by the short ladder against the wall and another formed by the long ladder against the wall.
First, let's identify the corresponding sides of the triangles:
- Short ladder: let's call its length "x".
- Wall: we know its length is 40 ft.
- Long ladder: its length is 60 ft.
Since the triangles are similar, we can set up the following proportion using the corresponding sides:
(short ladder length) / (wall length) = (long ladder length) / (wall length)
Substituting the given values:
x / 40 = 60 / 40
Now we can solve for x by cross-multiplying:
40x = 60 * 40
Dividing both sides by 40:
x = (60 * 40) / 40
Now we can calculate the length of the short ladder:
x = 60 ft
Therefore, the length of the short ladder is 60 ft.