The ladders shown below are standing against the wall at the same angle. How high up the wall does the go?
Use a proportion to find the missing side length in the following similar figures.
Ladder 1 is 14 feet tall, and the space between it and the wall makes up a right angle the height of this right angle is unknown. Ladder 2 is 5 feet tall and the space between it and the wall makes up a 4-foot tall right angle.
We can set up a proportion using the similar triangles formed by the ladders and the wall:
(height of unknown right angle) / 14 = 4 / 5
Cross-multiplying, we get:
(height of unknown right angle) = 56 / 5
So the height up the wall that the ladder goes is approximately 11.2 feet.
To find the height that the ladder goes up the wall, we can use the concept of similar figures and set up a proportion.
Let's represent the unknown height of the right angle in Ladder 1 as "x".
For Ladder 1:
Height of the right angle (x) / Height of the ladder (14 feet) = Height of the right angle (4 feet) / Height of the ladder (5 feet)
Setting up the proportion, we get:
x / 14 = 4 / 5
To solve for x, we can cross-multiply:
5x = 14 * 4
Multiply the numbers on the right side of the equation:
5x = 56
Now, divide both sides by 5 to isolate x:
x = 56 / 5
Simplifying the fraction:
x = 11.2
Therefore, the height up the wall that the ladder goes is 11.2 feet.