Question

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.

Answer 1

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:

`(4.2)/(3)=(x)/(9.5)`

We solve for "x" by multiplying both sides by 9.5:

`9.5*(4.2)/(3)=x`

Solving the operations:

`13.3=x`

Therefore, the 9.5 ft ladder is at a height of 13.3 ft.