A 9.5 ft ladder and a 3-ft ladder are leaning against the house the two ladders create angles of the same measure with the ground the 3-ft ladder has a height of 4.2 ft against the house.
we are given two ladders that form the same angle and both of them form a right triangle with a wall. The two triangles they form are similar and therefore each side is at the same ratio. We can use the following relationship:
Where "x" represents the height of the 9.5ft ladder, we have then:
[tex]\frac{4.2}{3}=\frac{x}{9.5}[/tex]
We solve for "x" by multiplying both sides by 9.5:
[tex]9.5\times\frac{4.2}{3}=x[/tex]
Solving the operations:
[tex]13.3=x[/tex]
Therefore, the 9.5 ft ladder is at a height of 13.3 ft.
