Question

A spotlight is mounted on the eaves of a house 20 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 15 feet. How long a ladder is needed so that an electrician can reach the place where the light is​ mounted?
Question content area bottom
Part 1
The length of the ladder needs to be
  
enter your response here ft.

Answer 1

To determine the length of the ladder needed to reach the spotlight mounted on the eaves of the house, we can visualize the scenario as a right triangle where:

- The vertical leg represents the height of the spotlight above the ground (20 feet).
- The horizontal leg represents the distance from the base of the house to the base of the ladder (15 feet).
- The ladder forms the hypotenuse of the right triangle.

We can use the Pythagorean theorem, which states that in a right triangle:

\[
a^2 + b^2 = c^2
\]

where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse (the length of the ladder in this case).

Here:
- \(a = 20\) feet (height of the spotlight),
- \(b = 15\) feet (distance from the house to the ladder).

We want to solve for \(c\) (length of the ladder):

\[
c^2 = a^2 + b^2
\]

Substituting the values into the equation gives us:

\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]

Now, take the square root of both sides to find \(c\):

\[
c = \sqrt{625}
\]
\[
c = 25
\]

Thus, the length of the ladder needed is **25 feet**.