Question

The ladders shown below are standing against the wall at the same angle. How high up the wall does the longer ladder go? All measurements are in feet.

Answer 1

Answer:

The longer ladder goes $x=12.5feet$ high up the wall.

Step-by-step explanation:

We know that the ladders are standing against the wall at the same angle.

Working with both triangles that the ladders form with the wall and the floor :

This triangles form the same angle respect to the floor.

This triangles also have a straight angle which we can notice in the graph.

Necessarily, their angles between the wall and the ladder must be equal.

Both triangles have the same angles and we can conclude that they are similar.

Exists a linear relationship between the correspondent sides.

For example, between the side of the ladder and the side against the wall :

$\frac{30}{x}=\frac{24}{10}$

or

$\frac{x}{30}=\frac{10}{24}$

Solving this for x :

$\frac{x}{30}=\frac{10}{24}$

$x=(\frac{10}{24}).(30)=12.5$

Given that all measurements are in feet , $x=12.5feet$

We also could find the value ''x'' applying the sine function in order to find the angle between the ladder and the floor in the smallest triangle. Then, with that angle, we could have applied the sine function in the bigger triangle to find the hight ''x''.

Answer 2

According to the given requirements in the image, 
let suppose x times the high up the wall longer ladder go
so,
30/24 = x/10

300/24 = x

x= 12.5