Question

2 points

6. The drawing below shows a ladder leaning against a building. Part B:
Suppose an identical ladder was put against a building that was 18 feet
high and the ladder reached the top of the building. How far away would
the bottom of the ladder be from the base of the building? Use
mathematics to justify your reasoning.
SUS
20 ft
CREARE
10 ft

Answer 1

4.9 feet

Explanation:

First, we need to determine the height of the building using the following:

`L^2 = H^2 + B^2`

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

`20^2 = H^2 + 10^2`

`400 = H^2 + 100`

`H^2 = 400 - 100`

`H^2 = 300`

`H = \sqrt{300`

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

`L_2^2 = H^2 + B_2^2`

Where

`L_2 = 18` --- Length of the second ladder

`H = \sqrt{300` ----- Height of the building

So, we have:

`18^2 = √(300)^2 + B_2^2`

`324 = 300 + B_2^2`

`B^2_2 = 324 - 300`

`B^2_2 = 24`

Solving for B2, we have:

`B_2 = \sqrt{24`

`B_2 = 4.9`