Question

John puts the base of a 9 foot ladder 5 feet from the wall of his house. How far up the wall does the ladder reach? Round your answer to two decimal places.

Answer 1

hello

to solve this question, let's draw up the situation

from the diagram, you can see the length of the ladder as 9ft and the distance between the wall and the base of the ladder as 5ft

to solve this problem, assuming it's a right angled triangle, we can easily use pythagorean theorem to solve this

(hypothenus)^2 = (adjacent)^2 + (opposite)^2

in this case,

hypothenus = 9

adjacent = 5

opposite = x

`\begin{gathered} z^2=x^2+y^2 \\ 9^2=x^2+5^2 \\ 81=x^2+25 \\ x^2=81-25 \\ x^2=56 \\ \text{take square root of both sides} \\ x=\sqrt[]{56} \\ x=7.48 \end{gathered}`

the length of the wall is 7.48ft