Question

A spotlight is mounted on the eaves of a house 45 feet above the ground a flower bed runs between the house and the sidewalk so the closest the ladder can be placed to the house is 28 feet how long a ladder is needed so that an electrician can reach place where the light is mounted The length of the ladder needs to be ?

Answer 1

The diagram representation is shown below

From the diagram above, it can be seen that the wall, the ground and the ladder form a right-angle triangle

To find the length x of the ladder needed, we use the Pythagorean theorem

The formula for the Pythagorean theorem is

$(\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2$

Where

$\begin{gathered} \text{Hypotenuse}=\text{xft}=\text{Length of the ladder needed} \\ \text{Opposite}=45ft=\text{Height of the house} \\ \text{Adjacent}=28ft=Ground\text{ length} \end{gathered}$

Substitute values into the Pythagorean theorem formula

$\begin{gathered} (\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2 \\ x^2=45^2+28^2=2025+784=2809 \\ x^2=2809 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{2809} \\ x=53ft \end{gathered}$

Hence, the ladder must be 53ft long