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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 ?

A spotlight is mounted on the eaves of a house 45 feet above the ground a flower bed-example-1
User Nathan Gonzalez
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1 Answer

23 votes
23 votes

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

A spotlight is mounted on the eaves of a house 45 feet above the ground a flower bed-example-1
User Senty
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